I'd say the current Irish-American identity that exists is about 100x stronger than any lingering french-canadian identity in the US, it was as total an assimilation as you could get really. That factor is actually sometimes brought up by french-canadian nationalists about how fragile french-canadian culture can be in a sea of english speakers.
My overall point is if Canada as a whole were conquered it wouldn't be a walk in the park but there is nothing so special about Qubecoise identity that they'd fight some prolonged guerrilla war decades longer than the english canadians.
At this point today a Quebec under the US for around a century would have some characteristics of the cajun regions of Louisiana.
It wasn't a simple process of assimilation. For one thing, about half of the migrants eventually returned to Quebec. Moreover, those who stayed congregated in French-speaking neighborhoods called "
Little Canadas" for a long time. What caused those neighborhoods to finally lose their identity was due to two factors: first, immigration from Quebec essentially stopped after the 1930s; second, there was a general push across the nation in the mid-20th century towards the assimilation of all immigrants. The period from c. 1930-60 was when a lot of American families stopped speaking their ancestral languages.
In Louisiana, francophone culture survived until demography worked against it: when the anglophone majority became large enough to dictate public policy by itself, it eliminated the francophones' legal rights. For the same to happen in Quebec (which had a larger total francophone population than Louisiana), you'd need a really large non-francophone migration there. As part of Canada in OTL, Quebec was the gateway to the rest of the country, and did in fact receive substantial immigration - but many of these immigrants (most notably the Irish) actually assimilated into francophone society, and others simply moved on to other parts of Canada.
If it is part of the U.S., Quebec might actually be a smaller initial immigrant destination than it was OTL - why go there when Ellis Island is closer? I suppose it could, conversely, receive a domestic migration of Americans, but I'm not certain what would draw them there. The climate's a lot colder than Louisiana's, and Quebec doesn't have oil.