The French have never been keen on leaving France. The only major wave of migration was that of my ancestors, the Huguenot, after the revocation of the Edict of Nantes by Louis XIV. Only a relative handful of French migrated to Quebec, especially compared to the hundreds of thousands English, Scots and even Germans who came to the British North American colonies. Even to promote colonisation of Algeria much of that migration came from Corsica or other French/Italian borderlands. There was no significant migration to French IndoChina or French tropical colonies. Certainly after the explusion of the Huguenots there was no religious minority looking for a way out nor true ethnic minorities seeking to leave. Rural nineteenth century France was largely a nation of small holders clinging to their traditional way of life in their pays, and often did not consider themselves to be 'French'. It is also no secret that to avoid further division of land holdings or domestic property the peasantry and the townsfolk limited families, hence the notorious population deficit of the 19th century. If their had been a larger population and a greater need or willingness to emigrate in the 19th century, I also think there is little doubt the government would have tried to direct the population movement to Algeria. Without Mothra sized butterflies (maybe no revolution, no Nappy, a much worse agricutural crisis/famine in the 1840's a la Irelande) I don't see any way to bring about a 'French wave' into the United States.