The thing was, French Louisiana was underpopulated. That's why it's so hard to imagine that TTL *Americans would sit in their little quarter and ignore the rest.
I think you'd see more in the Midwest and even see North Carolina and Tennessee developing earlier (no Civil War and slavery ending by the 1860s, etc.) than see the East Coast being too crowded.
One area I'd expect to be much more populous and prosperous is border cities like Memphis or East St. Louis. The latter in particular would anchor a major transnational metropolitan area (and no doubt have a much much much more positive reputation). This would draw people away from the coasts.