Why didn't France get Louisiana at the end of the American War of Independence?

I read a lot of comments about the colonies remaining under British protection if France still has a footprint on the continent.

why?

French population is miniscule compared to the colonies, and even in the French/indian war didn't go on the offensive. True that war was sparked by French claiming the Ohio Valley, which Britain wanted, but they were never in the position of being able to attack the colonies with intent to conquer and hold. meanwhile, the colonies had no problem with having a much more potent Britain to the north who had more cause and ability to attempt to regain territory.

At the end of the AR, the US didn't have the means to take what it had won (the northwest territories) let alone worry about the future shipping down the Mississippi.

Whereas Britain is the mother country with very real links in families, blood, culture, language, and religion; France was the true bogeyman of the Protestant world with monarchs who truly wanted to dominate the western world.

Throw in French regular troops were usually stationed in Canada and the Midwest since colonization while British troops were for the FIRST time stationed in the colonies in 1763 (and not merely during a war), and Britain's Canadian forces were usually miniscule outside of war after the Revolution, it's easy to complain but also easy to look at reality and deduce for all the hot air, Anglo-American relations were pretty peaceful overall.
 
Let's rather say that France was the only and real competitor Britain faced and that Britain wanted to be a monopolisted and could not bear such a competition.
 
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