Not Maine; that ship had sailed in 1783
So, how plausible would You call a Canada that includes Alaska, Maine, Saint-Pierre and Miquelon, and probably bought Greenland from Denmark?
What consequences would such a big Canada have on history, let`s say as from 1880?
Not Maine; that ship had sailed in 1783.
Alaska - if the Anglo-French expedition against Petropavlovsk in 1854 had gone to North America, rather than East Asia; more likely if someone other than Price is in command. The French will have to get something if the British get Canada; presumably, given the time frame, that could be concessions in Southeast Asia - perhaps British support for a French "protectorate" over Siam/Thailand;
Saint-Pierre and Miquelon - throw it into the Anglo-French settlement after the 1854-55 war; the trade here could be something in the Caribbean or Pacific where the British and French have conflicting claims; the New Hebrides comes to mind, although the 1850s is early for there to be much concern over them; somewhere in the West Indies seems more likely - maybe the British Virgin Islands, since control is already fragmented with the Danes.
Greenland - a British purchase in the 1860s in the aftermath of the Prusso-Danish war seems obvious, given the inability of the Danes to defend any of their overseas possessions; have the British "buy" the Faeroes, Iceland, Greenland, and the Danish Virgin Islands, and then transfer the DVI to France as a (belated) "final" installment on the St.P&M 'trade" mentioned above.
After Confederation, Alaska and Greenland each have territorial status within the Dominion; St.P&M becomes a county within Newfoundland, which presumably goes through its historical "colony-dominion-colony-province" evolution.
None of these territories are going to attract the European emigrants who went to NW Ontario and the Prairie Provinces historically in the post-Confederation era, so they remain largely empty in terms of Western settlement, beyond the trading factory-type; there are Canadian-government sponsored exploration and surveying efforts, and token (very token) garrisons of British/Canadian military and police/magistrates. One impact is the Canadian military and navy will have to develop into something more than a militia somewhat earlier than historically.
In the 1890s, the various gold rushes in Alaska and the Yukon are part and parcel of a single extended event that leaves a residue of "Canadian" national authority in place (commissioners, the RCMP/NWMP, etc.); in addition, the Dominion will get serious about having to maintain control of its frontiers, given the tens of thousands of miners and others flooding into these districts. The NWMP/RCMP vs the likes of Soapy Smith will become something of a national myth...
If there are not additional butterflies, in 1914-1918, the extractive industries will be developed as much as possible; there may be a token company of "Alaskan Rangers" or a section of "Greenland Scouts" in the CEF's order of battle, but not much more than that. The RCN will have a post-war mission of soveriegnty patrol and rescue/weather, more like the USCG in this era; the various civilian maritime agencies may all be folded into the RCN, since it (sort of) has a potential peacetime mission in this era.
The Depression will be tough in all these areas (as it was in Newfoundland) and there will be those in Canada who wonder why they bother. There may also be a series of public employment infrastructure development projects, particularly in Alaska, to create analogues to the Alcan Highway and the Alaska Railway project.
In 1939-45, the defense of Canadian Alaska and Greenland will be responsibility of the Dominion government, rather than the US; as such, this may actually lead to a smaller Canadian deployment overseas, since Alaska alone will require a substantial (in Canadian terms) garrison and naval and air forces worth the name, especially if the Japanese take a shot at the Aleutians; Greenland will be a focus of the RCN, not (as historically) the USCG.
The Canadian 1st Army of two corps and five divisions (historically) may only be the Canadian I Corps of four divisions in this scenario, which means it probably goes into action as part of the British army-level headquarters.
After the war, with Newfoundland's accession to the Dominion, events will probably transpire more or less historically in Greenland and Alaska; Cold War era defense spending, close ties to the US (US forces may be based in "Canadian" territory in this situation, unlike in reality), and in terms of economics, natural resource extraction (fishing, mining, lumber, etc.) until the energy boom of the 1970s, with the North Slope being developed in parallel to Alberta. Alaska probably gets provincial status in the 1960s or 1970s.
So, not huge differences, but significant.
Bonne chance