Among other things, the relatively late arrival of immigrant refugees from French Caribbean islands in the wake of uprisings, like on Saint-Domingue/Haiti. White Creoles lobbied to allow fleeing whites and their black slaves entrance specifically to revitalize French culture in the early 1800s, despite white fears of a slave rebellion inspired by the heroism of Toussaint Louverture and his comrades. The section on Haiti and the Black Republic in the Schomberg Center's online exhibit on The African-American Migration Experience here goes into it in some detail. So, basically, at least after the 1800s which is the era I know about, the influence was French Caribbean as French- the French speaking slaves and free black people of early New Orleans are obviously super important to the city's cultural development. (edit: accidentally had an "and" instead of a "/"- Saint-Domingue was one of Haiti's names under colonial rule, before it was declared the republic of Haiti in 1804.)

As a Detroit native, I can assure there's more "Frenchness" to the city of Detroit than just the name.

Numerous streets have French names: Gratiot, Beaubien, Lafayette, Dequindre, Livernois, and Vernier.

Numerous parks and place names have French names: Cadillac, Lafayette Plaisance, Belle Isle, Grosse Ile, and Grosse Pointe.

Outside of Wayne State are statues of French explorers Cadillac, Marquette, DeLaSalle, and Richard. There are many historical markers in English and French throughout the older part of the city. The Detroit Historical Museum has extensive displays on French history in Detroit.

Most interesting of all, Detroit's street design is modeled after Paris.

Unfortunately, Detroit suffered a devastating fire in 1805 which destroyed much of the city. Unlike New Orleans, Detroit was more of a military base and trading post and not much of a city. On top of that, the city frequently changed hands between the French, British, Americans, British, and back again. It wasn't really a place that tempted people to immigrate to it due to these factors. Therefore, the French community that was in Detroit was quite small. Once the Erie Canal opened up the Great Lakes to American trade, Detroit started to grow but with Americans from the northeast. "Suburbs" like Rochester and Utica were named after Rochester and Utica, New York due to this.

So, Detroit does have an extensive French history but also had many factors that made it quite easy for the French who lived there to remain small in number and to be culturally overrun in the early and mid-19th century.

Edit: In addition to French, British, and American sieges and attacks, Native Americans also contributed to the bellicosity of the Detroit area until after the War of 1812, thereby limiting early colonial immigration. And also, /u/BartletForPrez reminded me the Detroit city flag has both French symbols (fleur de lis) and English symbols (lions) to honor those aspects of its history.

I don't know what you mean by "there is no original Spanish culture in most of America's Spanish-named cities." Though immigration is responsible for a lot the Hispanic population in the American Southwest, there is also a fair amount of continuous occupation by people who have lived there since before the US took over. I'd argue that a lot of Southwestern culture is syncretic.

If you'd like some more reference to the French influence in North America, there's a great museum in Quebec City called the "Musée de l'Amérique Francophone" (http://www.mcq.org/en/maf/).

Incredibly large collection of objects and information that describe the history of French expansion down to Louisiana, including archaeological/historical artifacts from Missouri, Illinois, etc.

Hi. Former resident of St. Louis here.... (and yes, I recognize that by /r/askhistorians rules I'm not a source... so sticking primarily with facts that can be found on any decent map.)

There is a ton of French influence hidden all around the city. Districts, suburbs, and surrounding cities like Des Peres, Renault, etc are clearly French. Lots of local landmarks such as Fort de Chartres. Lots of French inspired architecture. Then there is the actual name of St. Louis, named after King Louis IX.... and that's just the stuff off the top of my head.

Lots and lots and lots of French influence in St. Louis if one looks around. Like a lot of other American cities, it WAS impacted by the influx of German immigrants in the later part of the 1800s. So I suppose that might be hiding it a bit.

Also, at least in California, many of the San xyz cities are named after a Spanish mission. Mission San Jose is actually in Fremont, for example. http://www.missionscalifornia.com/ has a lot more information on them.

This paper is likely of interest to you. The French population in the New World was never extraordinary. However, there was an entire class of French, a great number of whom were metis (half-Indian) who persisted longer than French colonialism as the support system and lifeblood of the Mississippi trade empire.

St. Louis and Detroit were French once, but Anglicized after France's defeat. The unique culture of New Orleans was founded by and dependent on the unique circumstances of French and metis traders. /u/StuMeat hit the nail on the head, as well; this community would be vastly expanded by an influx of French from the Carribean. But unlike other parts of the Mississippi route, like Mackinac, the French community persisted in New Orleans since colonization.

What are you considering to have "stuck" in New Orleans? The architecture? That's Spanish. The language? Cajun is Canadian and it's not really found in New Orleans. The tourist tchotchkes? The street names? The religion?

Perhaps the only thing that is remotely French is the civil law legal system, but even that is a uniquely American form that bears little resemblance to its French ancestor.