Unlikely.
In IRL, the American invasion of Quebec was a pretty decisive failure. Yes, Mongomery took Fort St. Johns and Montreal, but the Battle of Quebec (city) was a complete botch. If it had gone well and Quebec City had fallen, odds are that the Americans would just have been pushed out of Canada by the British reinforcements who were on their way to begin the counter-offensive down the Hudson valley. (American forces sent into Canada added up to some 1,200 men, whereas Burgoyne’s army was around 9,000 strong.)
As for why the French didn’t join the Americans, part of it has to do with the fact that the American occupation of Montreal became very unpopular both b/c the Americans had no hard currency to pay for supplies and because the American military governor General Wooster alienated the local population by arresting and jailing Loyalists and suspected Loyalists. Another part of it had to do with the fact that the French residents of Canada were Catholics, and the Americans tended to be pretty staunchly anti-Catholic as was seen in the reaction to the Quebec Act of 1774.