There's a Wikipedia article on French Americans, including colonial-era migrations, exchange with Canada, later arrivals (lots of French immigrants to California during the Gold Rush, for instance), etc.

Franco-Americans are less visible than other similarly sized ethnic groups and are relatively uncommon when compared to the size of France's population, or to the numbers of German, Italian, or English Americans. This is partly due to the tendency of Franco-American groups to identify more closely with North American regional identities such as French Canadian, Acadian, Brayon, Louisiana French (Cajun, Creole) than as a coherent group, but also because emigration from France during the 19th century was low compared to the rest of Europe. Consequently, there is less of a unified French American identity as with other European American ethnic groups, and French descent is highly concentrated in Louisiana and New England. Nevertheless, the French presence has had an outsized impact on American toponyms.

You could also read up on (or just check the Wikipedia page for) "Nouvelle France;" there's a section on the settlers. All around the Great Lakes and all the way down to the Gulf were French settlements, and the names are largely still there, just weirdly Anglicized. In Arkansas, "La Petit Roche" is Little Rock, there's a mountain called Petit Jean that's pronounced "Petty Gene," and (my favorite) "Aux Arcs" became "Ozarks." The French influence is still everywhere in the Louisiana Purchase area, it's just misspelled, mispronounced, or we've forgotten it was once French. It blended right in.

The French came not to settle but to make money. So many of the cities you name exist around French trading posts, but the French who lived there went back home as settlers from other countries moved in. The French did settle Louisiana and other places named elsewhere, but for many of them the goal wasn't to settle.

New England has a decently strong Acadian presence. But Acadians dont typically think of themselves as French, per se. They think of themselves as Acadian. The French influence is recognized of course, but its a different way of looking at ancestry.

You may enjoy reading about this linguistic offshoot, Missouri French!

The word you want to Google for is Cajun. That and the Louisiana Purchase.

You're overthinking it. Yes, we have immigrants from just about everywhere, but not every French-sounding city was founded by Francophones. Especially in the 19th century, non-English place names added a hint of poshness, because Americans of the time considered Europe to be the cultural center of the world.

Louisiana and northern Idaho being exceptions.

In some cases, they never went away. In New England - especially northern parts of Maine and New Hampshire, there are communities that are plurality Francophone, and have been Americans for generations. 

I think one thing that people often don’t understand is that American English is highly influenced by the French language - accounting for 30% of all words. Words like Lieutenant are pronounced differently in British and American because of the French influence. Or the word “herb” - Americans don’t pronounce the H just like the French.

As far as cultural things, of course the US is known for its wine. Napa Valley is one of the best wine regions in the world. Those wines consistently beat French and Italian wines in international competitions. Finger Lakes, as well. American cheeses like cheddar are very popular. There are entire states known for this, like Vermont and Wisconsin. I think in terms of bread, you see more influence from Italian and German breadbakers then French.

That said, French influence is just one of many patches on the rich tapestry that is America. It was impactful, but the influence was definitely overshadowed by groups like Irish, Italian, Polish, Chinese, and African Slaves - whose descendants have created our greatest modern cultural exports.

Isn't that where Creole and Cajun people came from?

It's interesting that you say that while using a French word like "cliché". Maybe it was intentional from you? :-D
And maybe reducing not having a strong French influence to not having a wine/bread/cheese culture is, you know, reductionist?