IMO the most likely outcome here is that the British recover Montreal and Quebec City, but the Americans end up winning their war anyhow. Both US and Canadian history will proceed rather differently thereafter.
But say Canada Libre makes it out of the war somehow. Either the Brits decide not to attack, or the expedition's commanding officer is one of /those/ generals, or they just roll snake-eyes. Whatever.
Now what?
Well, I think it's likely that QL joins the Articles of Confederation. Why not? It's a loose federation, and they'll still have plenty of autonomy. Note that Benedict Arnold was authorized to offer the Quebecois equal status with the other states. So, you have a "United States" that includes fourteen colonies -- at least at first.
But by 1787 the wheels are visibly coming off the AoC. So there'll probably be a Constitutional Convention, much as iOTL. And now things get hinky and ginchy. Do the Quebecois even join? Or do they simply walk away? I have trouble seeing much enthusiasm in Montreal for a More Perfect Union with the much more populous Anglo states. Other hand, if Canada stays in, this TL's Constitution may be very different from ours.
Again, I think the most likely outcome is that Canada either doesn't send delegates to the Con-Con, or doesn't ratify the subsequent document, and thus peacefully secedes And I think it would be peaceful; the country was profoundly war-weary in the 1780s, and the concept of "Union" hardly existed yet.
The map of North America looks rather different in this TL. The northeast corner of the continent is still British, and the Hudson's Bay Company will still be trying to claim the far northwest. What's now western Canada will eventually be the subject of a three-cornered dispute. My best guess is that Britain still manages to claim the modern Yukon Territory, while French Canada / Quebec expands into most of what's now Ontario (though the US may grab the southern "tongue" east of Lake Huron) and Manitoba. The
Pacific Coast, who knows.
If Canada stays in, then at least there's none of this nonsense about having a Senate that's fair and balanced between free and slave. Canada probably spawns a second and then a third Francophone state in the north. Quebecois would not be abolitionists, but they'd find the southern slave system deeply alien, and would have no interest in supporting it.
Assimilation, hmm. Probably not in Quebec itself. But there'd be some interesting mixing in the new western states. I suspect there'd be more movement south than north -- Canada has more land, but it's /cold/ -- so by the mid-19th century there'd be Francophone minorities in Ohio, Michigan and Indiana. Politically, the francophones would be natural Jeffersonian Democrats, so the political evolution of the US would be pretty different.
But, again, the most likely outcome is that the Americans hold Canada for a little while and then are driven out.
Doug M.