WI: USA and France split Canada & Maritimes after ARW.

The main thing I'm wondering with this thought experiment, is what happens in Quebec during the French Revolutionary Wars, and what happens between Quebec, the USA, and France if the Quasi-War still occurs and turns into a formally declared war between the USA and France?

So for the sake of this WI, let's assume the US performs better during the American Revolutionary War, and they are able to hold onto Quebec, while the Nova Scotia rebellion goes better and the USA is able to take the Maritimes in the Peace of Paris. In exchange for a partial reduction in US debt owed to France, they take the area that would have been Lower Canada. The US gets the area that would be Upper Canada, while the British retains Rupert's Land and Newfoundland. Spain takes the Floridas as per OTL, plus they still hold the Louisiana Territory.

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While the Debt owed to France is less due to trading Quebec, they still stop payments once the Monarchy is overthrown. Also, without the threat of a British invasion from the north, tensions between them and the US shouldn't be as high as OTL, and something like the Jay Treaty might be agreed upon slightly earlier.

Let's also say the French Revolution occurs ITTL. So what happens in Quebec, do they try to form their own country, and if so does France try and regain control? Does the US support an independence movement up north or stay out of it? If Quebec is back under French rule come the Quasi-War, does it become a front when that war goes hot? Does the USA attempt to annex it in that case?
 
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