AHC: France in control of the Thirteen Colonies

Your challenge, of thoust choose to take it upon thyself to abide by it, is to make France in control of the area formally known Thirteen Colonies, with a POD after the 17th Century. The British have to have colonized all thirteen before the POD, so it can't be a case of the French simply getting their first.

Bonus points if, somehow, the POD is after the ARW. I don't see this as very plausible though, so feel free to go before that.
 
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