What if the Quebecois could have been persuaded to be neutral in favor of the Patriots in the American Revolution? Maybe all that happens is that the British are defeated in the Quebec Campaign, and the locals don't make trouble for the occupying revolutionaries. Quebec sees the end of the war firmly under the aegis of the Continental Congress, but, being who they are, refuse to join the United States. Given their Francophone origins, the French allies insist that they be allowed self-determination in the same way the Americans sought theirs, and so Quebec remains separate from the U.S.
What happens then? Does it become its own republic? Is there any chance it might reconnect with France? (much more doubtful, given how the Quebecois viewed them as a parent who abandoned them to the Anglos) But maybe it becomes a popular destination during the French Revolution.