France was a low-emigration country in general:
"The French exceptionalism of small emigration was attributed to the French people's love of their land; for example, one French author wrote in 1860: 't must be recognized that the French rarely emigrate. The fact is that among the various races of Europe there is none with a greater regard for his native land than the French, with a more instinctive, more inviolable affection for his home, his village, and his country...Only religious or political persecution have led in France to emigration on a scale of any importance.'75 However, the key to the difference is to be found within the distinctive French pattern of economic development in the long nineteenth century, the major feature of which was the survival of a large agrarian sector. On the eve of the French Revolution, the productivity of workers employed in British agriculture was already well above that of the French; in familiar fashion, the more favorable British land-to-labor ratios fostered more capital-intensive agriculture, producing a surplus for urban investment, which in turn increased rural out-migration. But in France, the revolution 'gave the peasantry what they had long wanted--full rights of ownership and freedom from the burden of feudal exactions from all kinds.' 76 Although French agricultural output remained consistently below that of the British, the landless peasantry formed a far smaller proportion of the rural population. The characteristics of the agrarian sector in turn conditioned the pace and pattern of industrial development along different lines. Compared with Britain, the workshop sector in France survived much longer, and industry used much less unskilled labor. Most significantly for the present purpose, the rural exodus was long delayed. *The French could afford to love their land, so long as they kept their families small.* [my emphasis--DT]
"In short, France made the transition from agriculture to industry and from rural to urban life without experiencing the shock of the Great Transformation. Not only did fewer of the French leave France, but fewer also moved to great urban centers, because the push on rural localities was much weaker than elsewhere. If 'migration begets migration,' the reverse is true as well: the absence of emigration in the early period of transition makes it less likely that, should a 'push' subsequently arise, emigration will follow. Concomitantly, in the absence of surplus population, the state had no reason to turn emigrationist. Although the precocious limitation of fertility in the middle decades of the nineteenth century was rational from the economic perspective of the rural population, it was problematic in other respects. Hence, uniquely in Europe, from the middle of the century onward, the French state became decidedly immigrationist..."
http://books.google.com/books?id=Dqawo0Kpvz0C&pg=PA53
Incidentally, French emigration to the US may be less than official US figures indicate, according to the Harvard Encyclopedia of American Ethnic Groups (p. 380): "Before 1869, visitors--like Alexis de Toqueville--or merchants on tour were included in the tally. After this, US immigration authorities based their count on the country of last domicile, a practice that caused considerable error because many so-called French migrants were not French at all. Some of them were East Europeans who had temporarily settled in France, which, like the United States, has had a large immigrant population in modern times. Others were Germans who had acquired false papers in France; it had been easy for them to ross the Rhine where border controls were lax, but the more rigorous police regulations that prevailed in French seaports made it advisable for them to claim French nationality en route. American authorities counted such people as French citizens...French statisticians have estimated that only 75 percent of individuals listed as French by US immigration authorities were in fact born in France, but their sources are equally confused...In addition, the rate of return to France of French emigrants has always been high. The number of French people who actually decided to make their home in the United States may therefore be no more than half of what official US figures indicate, even if the total includes the natives of two regions that sent many immigrants to America: Savoy, which was Italian before 1861, and Alsace-Lorraine, which was under German rule from 1871 to 1918 (in 1920, one out of five French-born Americans was an Alsatian)." Anyway, the article continues, however one interprets the figures, they are quite small. "Norway, with one-tenth the population of France, has sent more migrants across the ocean."
And yet, despite their relatively small numbers compared to later immigrant groups, the French definitely did make an impact on the US, and not just in the New Orleans area:
"People, especially French and American people, tend to forget that the heart of the United States was once French. Not only was all of Canada and all of the Mississippi drainage from the Alleghenies to the Rockies under the French flag, as everybody knows, but French and French-Indian mountain men had penetrated to the West Coast before any of the officially recognized explorers and discoverers, for whom they were in fact often the guides. Deep in the Northern Rockies is the town of Coeur d’Alene, Idaho. In Nevada, Wyoming, Oregon, many of the leading merchants in the small towns are descended from the French, and they often still name their children Pierre, Jeanne and Yvonne — conspicuous among the recent rash of movie-star first names, dictated by the mysteries of Hollywood “numerology” which cause the Roman Catholic clergy such distress at baptism. Not only are towns all over the Middle West named such things as Prairie du Chien and Vincennes, not only are their leading families named Sublette and Le Sueur and Deslauriers, but — something very few people realize — French life survived intact in hundreds of small isolated communities until well into the twentieth century.
"When I was a boy, during the First World War, I took a canoe trip down the Kankakee River from near Chicago to the Mississippi. We passed through many villages where hardly an inhabitant spoke a word of English and where the only communication was the wandering tree-lined river and a single muddy, rutted road out to the highway. There is a book about it, Tales of a Vanishing River, and there was a popular humorous dialect poet, Drummond, who used to recite his poems in high-school assemblies and on the Chautauqua Circuit (a kind of pious variety tent show for farmers, now vanished) back in those days. “I am zee capitain of zee Marguerite vat zail zee Kankakee.” This was not off in the wilds somewhere — it was a long day’s walk from the neighborhood of Studs Lonigan..."
http://www.bopsecrets.org/rexroth/essays/frenchpoetry.htm