Well, for starters, you'd need a larger population, especially of soldiers. I'd say the best way is have the French victorious on Haiti (Louisiana was basically a grainery for Haiti) and then have the French troops who had won on Haiti (I think there were 50,000 of them or so) travel to Louisiana and stay there. Then, when the wars end, the troops will have been living there for 10 - 15 years. They call for their families and what not. Voila, now there's like 300,000 people in Louisiana.
Even at that, the population would be too small to maintain in the northern parts. Either Britain or the US would move across and capture most of it without fighting. So, I see Louisiana having about a 1/3 of a million people in 1825 and owning everything south of the Missouri River. Eventually, when Haiti collapses (it was bound to) you'll have another influx of about 50,000 planters. Immigration will probably be generally slow, maybe with some bursts in 1848 and other revolutions. Say, it would be interesting to see the effects of the king going into exile there...