Quebec/Canada was roughly doubling every generation primarily through natural growth as it was a healthy environment.
Louisiana, on the other hand, was not all that healthy, and was struggling to increase in population. The economy was primarily plantation, and a steady influx of immigrants, including slaves, was needed to maintain/increase population. Much of the French (Cajun) population actually came after the French period, with the influx of Acadians into the New Orleans region, and migration from Canada into St Louis. The "French Quarter" of New Orleans was built during the Spanish period after the original burnt down. And much of the population at the time of the US takeover was a result of relaxed trade restrictions during the Spanish period and the resultant immigration. New Orleans is known as a "French" city, but in reality is much more of a polyglot USAmerican city.
If we assume France settles New York, do we also assume that they ally with the Iroquois? If they do, NY has a very healthy environment, and will be the French center of the fur trade. You likely see similar immigration/colonial policies as in OTL Quebec, even though the climate is much more attractive. The heart of the Iroquois is upstate, while the heart of French population will be downstate in the NYC area, meaning the French won't be constantly wiped out as they were in Montreal/Quebec in the early going. Therefore, the French population gets a head start.
IF the rest of history goes as OTL and New France is lost similarly, I'd see NY as more like Quebec. We're positing a pretty major POD, though.