Your challenge, with a PoD after 1803, is to create a situation where French immigrants are the third largest group of immigrants during the great immigration waves of the 1830s and 1840s after the Irish and Germans. There should be sufficient French immigration for the French-Americans to form their own distinct urban and rural communities similar to the Irish, Germans, Finns, Swedes, Italians, Poles, Russians, and other European immigrant groups during the 19th century.
Where do you think they would most likely settle? What impact would a large French-American population have on US domestic and international politics?