The War for Independence is over. The new nation of the United States set about integrating all of that territory. This includes the former British territory of Quebec, Nova Scotia, New Brunswick, Prince Edward Island and what would become the State of Ontario. But the Articles of Confederation just were not working. So a new convention was called for a new constitution. At the end of it, things were set for the first Presidential election.
The implication is that the British are expelled from North America completely--from the continent that is, there is no hint the offshore islands of Bermuda and the Bahamas are lost to Britain, it would be most unlikely for the states in rebellion to manage that and if they had, I imagine they'd be mentioned here.
A nitpicker could point out that other footholds on North American continental ground remain or could be developed in countermeasure:
1) "Prince Rupert Land" is the claim to lands beyond the colonial territories claimed by seizure from the French in the "French and Indian War" as we called that theatre of the more global war ending in 1763, north of New France. Access to it was not I gather typically overland from the St Lawrence but rather by sailing directly to Hudson's Bay; PRL is essentially the domain of the Hudson Bay Company. Leaving this vast but not too hospitable territory out of the above list could be a reference to Britain managing to hold on to it in the treaty, with boundaries suitably adjusted.
2) Britain had also gotten ahold of "Florida" from Spain, and held it on paper and with some settlement in practice up to the ARW period. The boundaries were different, especially in the west--it was formally two territories, East Florida that IIRC was separated at the Apalachicola River from West Florida, whose boundaries were claimed considerably to the north of the current line separating the western state of Florida panhandle from Alabama, and reached far west of the current boundary separating Pensacola from Alabama's outlet onto the Gulf of Mexico at Mobile, as far as the Mississippi and thus including the coastal reaches of both Alabama and Mississippi and southeastern Louisiana. The western colony inherited less development. West of that, Spain was granted control of former New French claims west of the Mississippi including New Orleans and eventually developing Saint Louis as the Spanish center of power to provide what limited actual control of the claim border, made continuous with New Spain, the Spanish actually exercised there.
The outcome of the OTL Revolutionary War was for the British to return both Floridas to Spain, I suppose because the Americans insisted no second concentration of British force beyond their already threatening OTL retentions of what would become eastern Canada to the north; giving it back to Spain was an acceptable compromise, the Yankees being unable to press a direct claim on it themselves. North of the line considerably to the north of the current western state of Florida border which marked the former British West Florida northern limits of that claim, the USA got everything between the Mississippi and the Atlantic south of the Great Lakes and the southern boundary of ultimately Canadian claims. It did not take long, just a few decades, for various Yankee filibustering efforts to chip away at Spain's West Florida claims, to the point the Spanish reintegrated the remnant between Pensacola and Tallahassee back into East Florida, and eventually of course that too went the way of the western Florida Spanish claims...a combination of wildcat Yankee settlements purporting to found rouge republics, and the threat of US flagged forces sometimes invading purportedly to hunt down fugitive slaves, was an expensive and potentially humiliating gun to Spanish heads, which could go off in the form of formal war, invasion and conquest, not necessarily in that order, so that with such bad cops as Andrew Jackson lurking in the wings, slave-catching armies at the ready, the "good cops" of official envoys from Washington DC offering cash money for the honorable purchase of Florida looked sweeter, as well as an "offer you can't refuse" in the Corleone sense. But I suppose in the short run when the Treaty of Paris was negotiated, Spain did not look that weak and marginal to the British, especially in view of the fact that British North America remained a big gun pointed at Yankee heads, reinforced by Native American interests in checking the explosive potential of the expansionist former colonies.
Thus in principle, the fledgling USA, under wartime Articles of Confederation, could in principle make a clean sweep of OTL Canada to the north, but fail to secure Florida in the south, and possession being 9 points of the law, the British could either retain it directly, perhaps with adjusted boundaries, or alternatively as OTL hand it off to some other allied power.
Or the USA negotiators might find themselves beholden to allies of their own; I have to figure such a sweeping success as the Americans have evidently won here must owe something to European allies, mainly to France. OTL the French got little out of their support of the USA, in the Americas anyway...but of course the Yankees were doing well to get New York city and Georgia back, British forces were in occupation of other swathes of US territory as in Virginia on the eve of the cease fire, and the attempts to secure Canadian (to be anachronistic but convenient in terminology) colonies were fiascos. If the Yankees are in fact riding higher in the ATL when the peace is finally signed, it might be impossible to refuse the French some pound of flesh or other somewhere on the American continent--of course the French crown might not be interested in this to be sure, perhaps regarding the evident fiasco the British ultimately must swallow as evidence North American continental holdings are a bad investment.
The one thing we know for sure so far about possible French claims for services rendered the USA is that they do not get Quebec back. Otherwise--it is possible on paper they might get "Florida" for a certain value of Florida, for surely the Yankees will want at least some of it for themselves if they can get it. Taking all of what the British called East Florida between the wars would secure the entire Atlantic coast, denying any foe a land base from which to attack on that shore, assuming it is not titanic overreach to try to secure it. But granting West Florida to France, if Spain is not a neutral and in a position to have costs imposed on her too, involving perhaps restoration of New Orleans, or even all the way up to St Louis and beyond west of the Mississippi.
The title of the thread though strongly implies the Yankees come out of the war in a sweepingly nigh-invulnerable position, so even if France does get a substantial set of North American territories--clearly all in the south if this happens at all--the USA is in a position of high self-satisfaction, and I don't think French possession would reach far up the river. Also granting them sweeping control of the entire Gulf Coast, even if restricted to West Florida only, is not something the Yankees would prefer.
Here's the scenario I am sketching out based on the slim evidence of one post so far:
1) the exact POD is up in the air, but it appears likely to be sometime after the outbreak of war between British authorities and the New England Colonies in 1775, and very likely to relate to the attempt to conquer Canada of OTL, being far more successful in this TL. OTL the colonies in rebellion, now "states," attempted to make a clean sweep of the colonies on the continent starting with fomenting and supporting uprisings in the Maritimes and the seizure of the named British colonies to the north of New England, which in the ATL might be considered part of a larger New England. To do this, the plan involved a major invasion force taking Montreal, as Wolfe had done (dying in the process) on behalf of Britain with largely colonial forces in the previous war. Presumably this particular scheme pays off, and either as a knock on or in parallel, the rising of colonists in New Brunswick, PEI and Nova Scotia also falls into line with the Continental scheme; this would have to rely on heavy local support, but I think that was somewhat forthcoming OTL and would be reinforced naturally by victory. However I would guess the British are well able to retain Halifax itself, due to heavy fortifications and a high priority on its retention being placed there, and its ability to be supplied and reinforced or evacuated by sea. Also, I would be surprised if the Yankees could take Newfoundland by simple conquest; the main population is on the island, and the Labrador mainland part is pretty peripheral and hard to hold without expensive expeditions. So British sea access is pretty well guaranteed I think and even sweeping success inland to the west still leaves the USA in rebellion with a heavy military distraction keeping Halifax besieged, and the British having the power to raid and land on the coasts pretty much at will. Securing Anglophone east Canada (as we know it today) would thus be militarily incomplete.
Quebec would require some finesse to hold. The OTL Declaration of Independence (which might be at least somewhat edited by butterflies here, or might be exactly as OTL) mentions the alleged tyranny of British power over Quebec, but mainly to stress it is an arm of force brought against the colonists. In fact the manner of British rule over the formerly New French Francophone Catholic there was I gather, accomplished pretty diplomatically, though perhaps with an alarming disregard to British colonial custom--alarming to the Anglo-Colonials on the Atlantic coast that is, to the former French subjects it would be little change. The British viceroys in fact took steps to avoid annoying them, and I gather the clerical power structure of the hegemonic Catholic hierarchy was much put at ease and might actually have found British rule preferable. Nor was there mass discontent among the peasant settlers on the Saint Lawrence. To the properly "quebecois" francophones then, the American invasion would indeed seem alien and potentially quite threatening to a perfectly acceptable status quo. Therefore the envoys of the Continental government would have to be quite astute and diplomatic in their turn merely to prevent the Quebecois from being an actively anti-Revolutionary force and sitting on them by force would be quite distracting in terms of tying down potentially fighting forces on occupation duty.
Being humanistic and optimistic about the best ideals of American revolutionary ideology, I personally hope the resolution involves a combination of short term visibly dominant local force, what with the cooperation of the Maritime colonists also in rebellion downstream, strong force in Quebec city, Montreal and other strategic points, and longer term persuasion of various factions, including some Anglophones, that the American republic is the future and they have an honored place in it if they join in. The Catholic hierarchy has something to fear to lose and little apparent to gain, but in fact while anti-"Papist" bigotry was a major thing among the Anglo-American colonists, there were OTL some Catholic signatories of both the Declaration and the Constitution at the Convention. Therefore I figure that in the right circumstances, having chosen suitably statesmanlike envoys with suitable authority over potentially bigoted Continental and expeditionary State forces to keep rein on them, the powers that be in Quebec are persuaded to form a State of their own, which is received in the Continental Congress as equal to any other. In fact Quebec elites are proficient enough in English to function as envoys of their state in the English speaking United States In Congress Assembled (if that terminology survives the POD) but there will be no question of imposing English only; Quebec's internal state business will be conducted in French primarily, though surely with extensive translation into English taken for granted. Of course any formerly British-American colonial with pretensions of high culture would be more or less proficient in French themselves, so even Congress might get notably bilingual. De facto, I suspect Quebec will be more theocratic than the Atlantic colonials like and a certain degree of anti-Catholic bigotry will remain a thing, but somewhat toned down versus OTL, and over time I expect democratic republicanism will assert itself against clerical pretensions of power and authority, both by persons radically opposed to Church authority and even the Church itself, and by persons professing seriously continued faith and fidelity nevertheless asserting also the secular separation of church and state even in Quebec.
The Constitution of OTL, which I suppose will be significantly butterflied here, does not in any way forbid individual states from establishing churches--what did that before the Civil War, with disestablishment universal before the 1830s were out, was political expediency. I believe the "equal protection" clause of the 14th Amendment would render modern establishments legally impossible nowadays, but any Constitutional barrier to it does not stem from the Bill of Rights directly--I do think that in the context of the Equal Protection clause, the prohibition on establishment placed on the Federal government is logically extended with the Bill of Right's moral authority to the states as well. Of course the ATL Constitution and its subsequent evolution is probably quite butterflied and subject to a great many variations! Demanding the Quebec establishments accept radical secularism as an imposed doctrine this early however would be undiplomatic and counterproductive--again I imagine Quebec coming into line with the range of US practice gradually over time. And the Catholic Church retaining pretty strong authority through legally informal means pretty much indefinitely, unless the population is swamped out by non-Catholic immigrants, which i do not foresee except in limited sections of its boundaries if that.
Parallel to the suggestion that Quebec be incorporated as a state with a distinct nature initially to accommodate its peculiarities versus a typical British North American settler colony, I also put in a brief plea the author consider the possibility that with the situation of Native American people being different than OTL with Yankee sweeping successes, rather than simply turning the screws of OTL tragic near-genocide somewhat tighter, that a possible reaction is that at least some Native peoples, seeing they cannot as OTL expect effective British aid against the onslaught of Yankee expansionism, instead of despairing and desperately fighting a hopeless cause, negotiate some kind of terms with the Patriots, even going so far as to risk fighting their own long term interest in actively aiding the Rebel cause in order to solidify meaningful support among some US people, and as a result first the self-selected few who come to these terms and eventually all surviving Native peoples, including those who initially fought against the USA but eventually surrendered, will have some sort of negotiated Constitutional status better than merely subjected alien peoples, but rather some recognized role in the Constitutional order that secures them some rights and some resources reserved to them, in return for their compliance.
I have a dear quaint hobbyhorse notion you see, of an Indian Confederation forming which legally unites disparate, multinational, discontiguous tracts of treaty granted territory under the formal banner of a state-equivalent nationwide body, in which the Native peoples collectively have equal representation proportional to total population of all their peoples combined in the House of Representatives, and two Senators in that house, and voting for President on the same basis as Anglo and other European descended citizens. Few Native peoples ever had a population as distinct nation-tribes comparable to a US state, even a very small one, you see. But integrated all together they would in fact have numbers to amount to a fair sized if not too large US state. Of course internally such an Indian Confederation would be nothing like a US state, not being an integrated and distinct territorial unit nor composed of a large majority of more or less culturally unified people, but rather a crazy quilt patchwork of tiny (in population, I envision tribal lands tending to span somewhat more territory, and better land, than OTL) reservations each autonomously ruled by quite distinct Native customs as evolved in their encounter with their conquerors. The Confederation would be a clearinghouse negotiating intertribal conflicts where these arise, and mainly mediating with state scale authority the relations of each tribe with whichever states they are embedded within or between. It would itself therefore require a federal structure internally. But being able to collectively bargain with the Federal regime I think would tend in the long run to negotiate a more reasonable settlement for each tribe and contribute to the collective dignity of all Native peoples. (They would be called "Indians" of course, and if this scheme were to evolve to work as advertised, the "Indian" label would have more dignity than OTL so that term would remain the standard way to politely and respectfully refer to North American Native peoples in the ATL). Legally speaking their status would evolve from foreign peoples who have separate treaties with the US federal government toward those treaties being amended en masse and subsequently to negotiate their incorporation as US citizens with special negotiated status but the same general rights and duties as other citizens broadly speaking--both their distinctiveness and their assimilation would be legally defined and enforced. In the long run I would expect somewhat higher overall "Indian" populations than we recognize now, both because of overall lower death rate, and because Native peoples in charge by basic treaty template of identifying who belongs in their distinct nations at their own discretion instead of Federal top down mandate will be more inclusive, and people who OTL either tried to keep their Native connections quiet or were completely ignorant of them would be more likely to embrace the identity, and be accepted by their respective peoples.
To return to the broader picture having entered this plea for consideration, or that might inspire some other approach toward a different, hopefully better outcome for Native people:
So--first of all, the major base on land, and connection to power projection against the USA via arming and organizing Native American resistance, of Britain OTL is short circuited out and denied, and to a limited extent manpower OTL in British hands also becomes available to the Continental cause. Against this a siege of Halifax probably needs to be kept up unbroken throughout the war.
The War I believe will be of considerably longer duration than the OTL war, which was already the most enduring war in terms of time span of any US war of OTL, unless one counts every phase of the US entanglement in Southeast Asia known as "the Vietnam War" or the ongoing occupations in Iraq and Afghanistan as of today. Which is telling--all are essentially the same kind of conflict, with the USA on the insurgent side in the 18th century OTL and on the imperialist side in the 20th and 21st century conflicts.
What is different here is that early success in "Canada" to again use a convenient anachronism will inflate Yankee ambition. I would think early and sweeping if not complete success would on the whole enhance US capability--mainly through tipping the balance of political calculation toward the secessionist "Patriot" side, lowering the percentage who remain deeply "Loyalist"/"Tory" and shifting people who OTL devoutly equivocated to avoid entanglement and being on the wrong, losing side as much as possible, toward the Patriots. Secondarily by largely though not entirely removing the threat of counter invasion from the north, permitting heavier concentration of total American potentials toward resisting descents on the coasts and toward the southern front, and to a quite limited extent by increasing the pool of available manpower with recruits from the Maritimes and Quebec. Against this, the British will be somewhat more enraged and determined, persons who OTL got away with openly defending American interests and denouncing British imperial ones in Britain, such as Edmund Burke, will be more quelled and either prudently keep their heads down or perhaps have them lopped off, or are otherwise legally clamped down on. The British will retain Newfoundland and Halifax and the Atlantic islands of Bermuda and the Bahamas as well as Caribbean holdings--perhaps in a long war with more resources, the US will develop some serious naval resources to challenge British control of the Atlantic islands, attempt interference with British shipping across the North Atlantic, and go raiding in the Caribbean and farther afield. But I would guess that this remains at serious disadvantage to RN power throughout and such attempts impose some costs but are not successful in terms of actual sustained conquest.
Nevertheless, such war aims as securing Florida, however defined, to deny a British foothold on the continent and round out US coastal defense, and demanding at the peace table the abandonment of all British and to the extent possible allied claims anywhere north or east of Mexico, including Prince Rupert Land and Newfoundland as well as surrendering Halifax, will come to be the American policy, and it is this extreme they hold out for that sustains the war perhaps twice as long as OTL.
From the quote of the OP I open with, I infer, perhaps wrongly, that in this TL, the end of the Revolutionary War and adoption of the new Constitution are telescoped together as they were not OTL. OTL, the Articles of Confederation were only briefly fully adopted by all US states in formal legal force before the new Constitution superseded them...but informally, the Articles, preceded by informal ad hoc measures leading to them, were de facto the government of the USA from before the Declaration right up to the Constitution being ratified. And this long period included not only the ARW years but a comparably long post-war period of nearly a decade, in which time the USA, nominally and legally at peace with the Treaty of Paris ratified by all sides, evolved some key features of government and administration carried over into the Constitution, notably Jefferson's Northwest Ordinances laying groundwork for how the USA would incorporate and govern Territories on a path to statehood (thus settling a lot of conflicting and otherwise unsatisfactory state claims to territory beyond the traditional state boundaries.
But here, I gather that the war goes on much longer due to the factors mentioned above, with the Articles regime, probably much modified versus OTL both by formally agreed to amendment and also by de facto practices not formally ratified, being shaken down into a more or less workable Federal government. One might suggest an outcome of that would be not to have a new Constitution with a clean sheet, but rather to simply extend a half-assed but working Articles frame into the indefinite future. But it is not implausible a new clean sheet Constitution would also emerge from the war years, with the matter of adopting it and even fleshing out much of its detailed nature accomplished diplomatically during the war but placed on hold by mutual agreement until that war is won, and then by prior agreement rapidly adopting it as the ink dries on the peace treaty.
The resulting Constitution might plausibly be closely parallel to our own, or might be radically different in some details or the entire structure. Above in sketching the "Indian Confederation" concept for Federal incorporation of native peoples simply assumed, for illustration's sake, exactly the OTL outcomes in terms of House of Representatives, a fixed uniform number of Senators for each state, and Presidential EV at state discretion via choosing a number of Electors equal to their total Congress representation all as OTL--but I hardly assume it will be exactly that way; quite a few curve balls, of subtle detail or gross structure, will probably come at us taking us on a different track.
Everything I have written here is a pretty personal extrapolation I have spun to try to match my own concepts of the nature of things in North America in these days with the limited sketch we have been given so far.
I look forward to the author revealing their own thinking.