Firstly, no, as I mentioned, French engagement in N.America was systemically different than English engagement historically. Changing the outcome of the French Revolution like this does not mean that policy is going to change, and given that this is explicitly a moderate to conservative regime that means pre-revolution policies are MORE LIKELY, not LESS LIKELY to be continued, which includes non-colonization of N.America. To claim otherwise you'd need to show that those involved in this alt-timeline EXPLICITLY wanted to increase colonization into N.America in opposition to all French policy both of the Monarchy and later Empire.
. . . You really have no idea of the sheer scale of the Irish migration to N.America, do you? The French fleet, as it was, could in no way support that level of immigration, and New Orleans and the Louisiana territory could also in no way support or absorb the level of immigration we saw in the OTL. We're talking over a million Irish immigrating to the US in a few decades, and a depopulation of Ireland to the extent that in modern times there are more people of Irish decent in the United States THAN IN IRELAND. And again, there's literally NO REASON for said Irish to immigrate to Louisiana. There's no jobs. The farmland there is not suited to the type of farming they're used to, and you're dealing with an area where white migrants tended to die by the tens of thousands due to malaria (one of the major reasons for African slaves being so valued in the American south and Caribbean was their genetic resistance to malaria that EUROPEANS LACKED). And bear in mind, large parts of Louisiana where they would be initially migrating to IS A SWAMP which is prime breeding ground for mosquitoes. Oh, and did I mention that New Orleans periodically gets hit by hurricanes, as in, almost yearly? That's a BIG DAMPER on building up a city especially before the advent of modern weather forcasting.
Basically put, there is literally no reason to migrate to Louisiana when you can migrate to New York or Boston. Weather is better and more familiar there, farmland in the New England, Mid Atlantic and Old Northwest more familiar, and there's way more job opportunities from the new factories opening up in those regions. None of which Louisiana has, nor would the French develop there as Louisiana is piss poor for industrialization with no good fall lines for pre-steam powered mills, and far removed from any coal reserves for steam powered industrialization of the later half of the 19th century. There's a REASON Louisianan is a agricultural and shipping state IRL, and it's because it's one of the WORST PLACES for industrialization on the continent, between swamps, hurricanes periodically destroying everything, disease, and yeah. Frankly, if it wasn't the mouth of the largest navigable river system in the world, New Orleans would never have been settled where it was.
Long story short: there is literally no advantage to France to hold onto the Louisiana territory in this timeline. It doesn't have access to good raw materials, it doesn't provide access to good farmland that generates valuable crops. To develop it would cost continual money and need continual rebuilding from regular large storms that other locations do no suffer from, and to really develop it would require a level of commitment and population pressure that France, even in this timeline, likely does not have...
And finally, after doing more research on it, this entire point is moot. France doesn't even control Louisiana. It was under Spain's control per the
1763 Treaty of Paris and the
Treaty of Fontainebleau. After the American Revolution the the Peace of Paris, north America looked like this:
Note who's nowhere on the map as a major player: France.
So the question becomes would this French government pursue a similar arrangement to Napoleon and the
Third Treaty of San Ildefonso in 1800, that saw the return of Louisiana to the French for territory in Italy. The events leading up to these territory exchanges are all part of the complicated fallout of the French Revolution, so it seems unlikely that the EXACT same exchange takes place. As such, it might end up that there's a Spanish-American War sometime around 1810s over Louisiana rather than the Quasi War and Britain vs US War of 1812...