I always wondered why this didn't happen. After the Seven Years War, France gave up tons of territory in North America. In the Revolutionary War, why didn't they try to take some of it back? I don't think the Quebecois would have minded being under French control again.
Assuming the U.S. gets the same territory it did OTL, what happens next? Do the British try to take Quebec away from France again during the Napoleonic Wars in Europe? Is there a Quasi-War in this time, considering the U.S. can now threaten French territory.