Did a bit of an update on an old map for an internet project I'm working on, so I thought I might as well post it.
Based (a bit loosely [1]) on H.R. Percy's "Letter from America", in the Sandra Ley-edited "Beyond Time" collection.
The French were more successful in their colonial efforts early on, Louis XIV getting the colonization bug from some of his advisors and after the 1670s spent some money on funding colonization efforts as well as wars and ornamental fountains, moving "underemployed" French groups to the Americas rather than using them as forced labor Colbert-style at home, while some key naval victories in the 1690s and early 1700s left all of what we would call the Canadian Maritimes in French hands. This gave French America enough of a demographic and geographical edge by the mid-18th century to win the equivalent of the French and Indian wars, confirming French control of Louisiana and Canada and pinning the British colonies east of the Appalachians. Another demographic boost came after an alt-French revolution, with the French monarchy fleeing to America like the Portuguese in Brazil in our world, followed by a cavalcade of loyalists. A generation later, the monarchy returned to Europe, and the colonists did not greatly appreciate returning to "exploited colony" status after being the center of the French world for a while.
New France would afore too long rise in revolt, joined and supported in a pan-north American effort to expel European overlords by some of the British colonies (they'd already tried once to break away, and been crushed [2]), and afterwards a "republican union" of the French and British colonies would take place. Alas, the British colonies, ravaged by the struggle (which had been as much a civil war as a revolt against British rule), soon found themselves the junior partner: revolts against French dominance began as early as the 1860s, which led to repression, which led to more revolts...French-Anglo conflict was a serious internal problem for a long time, with separatist terrorism taking place as late as the 1970s, but rapid economic growth over the last four decades and some political compromises have greatly lessened tensions by 2010 (although visitors from the French-majority states grumble a great deal about everything having to be bilingual in New France while the "Onglays" can't be bothered to learn good French).
The French-speaking population has been boosted by a very open policy towards Catholic immigrants from wherever, while the English-speaking regions have generally been less attractive to settlers due to native hostility to non-Protestants and political turbulence. People descended from English-speaking populations (well, English, Scots, and anglified Irish and Welsh) still make up over 25% of the population of New France, but only 17% or so of the population speak English as a first language, including third-language speakers and their descendants settled in the Anglophone majority eastern provinces: people whose ancestors mostly came from the British isles are scattered far and wide across New France, but cultural and economic pressures mean that those who move outside the "Old Six" generally abandon English for French within a generation. Native Americans have generally done better than in our world, although the government has long tried to make good French-speaking Catholics of them (there are a _lot_ of what we would call "Metis" people), and there are some huge areas at least theoretically belonging to the Amerindian nations. [3] The black population is also somewhat better assimilated than in our US (slavery came to an end in the 1870s fairly peacefully, the institution never having become as deeply rooted in New France as it did in the southern US of our world.)
The Republic was the leader of a coalition of nations in a cold-war type situation versus the Russian-led Collectivist Union, similar to Soviet Communism but bigger on anti-nationalism and Maoist popular mobilization. The Union has recently collapsed, rather more messily than our Soviet Union, and political fragmentation and civil wars are still ongoing.
Important allies include China, a 40% Christian (more or less: there are some odd local offshoots) republic - a working democracy, but a protectionist, import-substituting, bureaucratic one whose "lite socialism" has left the country, like our world's India, relatively poor. And then there is the empire of Japan, "bastards, but our bastards" while the conflict with the Collectivists was going on, but now increasingly a *fascistic embarrassment. The Republic of Great Britain [4] has a relationship with New France as prickly as our world's France has with the US, but is still an ally and militarily formidable. The kingdom of France is nowadays something a satellite of its overgrown offspring.
Central Europe is still scarred by the Short War of '77, which involved both chemical and radiological weapons. Post-war, the Allied Powers created the "MittelEuropa Recovery Zone" as a framework for the economic rebuilding of the region, which been renamed the "MittelEuropa Development Zone" as the local economy has picked up: the expansion of the union to the rest of western Europe has been often talked about, but the current free-trade regime seems sufficient to most without adding in a meddlesome Prague bureaucracy.
Latin America is more closely economically tied to New France than it is with the US OTL - free-trade arrangements with fellow Catholics and Latins came into effect fairly early on. [5] The Spanish Empire's efforts to devolve control in Latin America by creating sub-kingdoms within a overall Spanish Empire were only partly successful, with much of Latin America eventually going republican (or beyond, in the case of Gran Columbia, which is an anarcho-socialist republic).
Africa is largely post-colonial, only the Italians holding stubbornly onto their mineral-rich holdings. It is broken up into somewhat fewer and larger chunks than in our world, some pro-democracy (at least in theory), some still Collectivist, more English and Dutch and less French(French colonization efforts were confined here to North Africa and the Senegal-through-central-Sahel area). South Africa, never snatched from the Netherlands by Britain, is a loose federation of African and Dutch (well, at least Dutch/Boer-speaking-plurality) states. The continent is poor and messed up, but not as relatively badly off as in our world.
The Arab Federation is more or less a democracy, but oddly the same party keeps winning the elections(although at least the Presidents don't overstay their terms). The south Indian republic is a prosperous democracy, and formed a keystone in the Indian Ocean portion of the democratic alliance's military plans: it still hosts a lot of British and New French troops, since the North Indian situation is to say the least fluid.
Democratic leftism is more anarchist, anti-state than OTL, and has even less patience with the Collectivists than our Social Democrats had with the Communists. Technology is a bit behind our timeline, varying from late 1960s to mid-80s depending on the field: the first satellite wasn't put in orbit until 1983, and nobody has been to the moon.
[1] Although we do have an unreliable narrator, there was a definite smell of "French America is greatly inferior to British America! The Commies are going to do much, much better with weak-ass French north America rather than the US" about the story which I found a bit annoying. Not to mention the bits about the French putting black French-speakers above white English speakers and using Indian troops to repress said English speakers come across as a bit triggery nowadays, although I suppose this could be interpreted as progressive "historical irony" if you squint.
[2] Struggling to finance their long struggle with revolutionary France, Great Britain squeezed their American colonies pretty hard.
[3] In actually practice, if a mining or timber company wants rights, the Federal government will give it to them, and the indigenous inhabitants don't get much choice in the matter, although they at least they get a slice of the profits if they don't complain too much.
[4] Britain had a rather more troubled 19th century than in our world.
[5] Not that relations always have been rosy. New French corporations have been voracious in their exploitation of Latin American resources, generating a great deal of populist resentment towards Le Colosse du Nord.