So, another Louis making same thoughtless decisions, why would it be different fromIn OTL, France didn't aid the colonists in their war against Great Britain because they thought that America would be a great ally and all that. No, they did it because it would weaken Great Britain, their worst rival, especially after the British got really powerful after the Seven Years' War.
Great Britain gave away Canada because they had lost a war in which the French had gained several decisive victories- the French were in a really good position during the peace talks. They also had lost all of their lands in India to France- now, what do you think the British care about more? The cold forests of Canada, which had a bunch of French speakers and French people anyway, or the rich and lucrative lands of India? Kind of like after the Seven Years' War, Britain offered to give France back Quebec in exchange for the sugar islands in the Caribbean. The French declined because the sugar islands were more profitable.
In OTL, France had the money to deploy troops to the Colonies and chose to not deploy them to Canada to take it for themselves either. In 18th and 19th century warfare, most of the time you would capture a place that your enemy liked and once the war was over, offer to give it back in exchange for a different place- one that you like. The French could have captured Canada and demand it to stay in French hands if they wanted to, but that would mean France vs Britain only, as the Americans were too busy trying to get the Brits out of the colonies themselves. The alternative was sending French soldiers to India, where their strong Mysorean allies would be able to help capture one of Britain's most important colonies.
OTL's France, I just don't see the logic there .