Canadian, rather than American, but there’s 2 or 3 separate anime about Anne of Green Gables. (Japanese people LOVE Anne, for some reason…)
This doesn’t exactly fit the OP since it’s a silent film, but there’s a two part German version of The Last of the Mohicansfrom 1920. I mention it mainly because it features Bela Lugosi as Chingachgook (and because Lederstrumpf sounds vaguely obscene).
I taught English in Japan for a whole, and one of my students was a woman who said her ultimate goal for learning English was to be able to read Anne of Green Gables in the original language. She had a dog named Matthew, after the character in the book.
I feel like there must be some anime series set in Europe, although I don’t know enough to name any. (I want to say there was one about Marie Antoinette?) I know of several anime series that take place in a fantasy setting that resembles Europe, but that’s not quite the same thing as using a real country and its historic figures or well-known literary characters.
I remember seeing posters in Japan for productions Western musicals such as Le Mis, Elisabeth, and a stage version of 8 Femmes. I could see from the posters that these shows had all Asian (presumable all Japanese) casts, but I don’t know if they were performed in the original English/German/French or translated into Japanese.
It’s not about an American, but the Hong Kong Action Film Vengeance stars French signer Johnny Hallyday. He plays a Frenchman but speaks (fluent) English throughout the film, which (in the version I saw at the theatre) was in Cantonese with English subtitles.
The first thought for me was anime. I’ve seen series set in America, Ireland, Europe, based on various well-known mythologies from those cultures, with everyone speaking Japanese. And I seem to remember some oddness with Return of the Dragon - set in Greece but darn near everyone speaking Cantonese except the monosyllabic Chuck Norris.
I seem to recall a French version of the book Payback was based on as well.
The Brits made a mystery series based on some Italian books with Rufus Sewell set in Italy with a cast chock-full of Italians, and everyone speaks English. Hell, I don’t think Sewell even attempted an accent.
You think Lederstrumpf sounds obscene? How about Chingachgook, die grosse Schlange? 
Quite a few Chinese films set in America use little or no English:
Once upon a time in china and America
The Chinatown kid
That seems to be wondering off the mark. It was a French movie set in France that just had a character who spoke English.
Getting off track myself, but I watched The Thieves a few months back and I could tell I was missing some of the plot. It was a Korean movie set in Macao and the story was about two groups of thieves, one Korean and one Chinese, who had to work together to rob a casino. The movie was subtitled in English but the languages used by the characters were Korean, Cantonese, Mandarin, Japanese, and English - and there were a lot of character interactions based on what language was being spoken.
I’ve seen it, and it did have a lot of German immigrants in 3rd class and a heroic German First Officer & his girlfriend. Oddly the *Strauses * were still referenced.
But in a twist ending it turned out they had been secretly plotting with the iceberg.
“Goldberg…Iceberg…what’s the difference?”
Not to mention some of the other characters in the film: Harry Hurry, Wahtawa, Gespaltene Eiche, Pfeilspitze, and Flinker Elch.
Here’s Die Schatzinsel (Treasure Island) in German (2007).
Purple Noon, 1960: a version of The Talented Mr. Ripley, in French. Alain Delon plays the American Tom Ripley.
“Killer Condom”.
It takes place in New-York City, all the chars are American, but it’s German-made and the whole cast is German-speaking.
Some Laurel & Hardy shorts were filmed in both English and Spanish. Not just dubbed, actually filmed in both.
Just last year there was a German version of Huck Finn. Trailer. It was sufficiently popular that it was shown on a Lufthansa flight I was taking, and yes, it was beyond weird to see 19th century characters on the banks of the Mississippi speaking auf deutsch.
I’m sure there are plenty of people who are intellectually lazy, but there are good reasons to avoid subtitles in film. I dislike watching movies with subtitles. It’s not because I dislike reading. I read many things. It’s because film is a visual medium, and if I’m constantly looking down at the words I’m missing the subtleties of the scene.
I watched both the American and the Swedish versions of Girl with the Dragon Tattoo. Both fine films. But I enjoyed the American one way more. The genre magnified the shortcomings of not speaking the language. Mysteries and detective stories often hinge on small details and careful examination. You have to look for the small holes in people’s stories and catch the shot that lingers just slightly too long on a clue. All of which is close to impossible if you’re reading a translation at the bottom of the screen and missing all the nuances of the performance and the cinematography.
The Passion of the Christ.
God is an American, isn’t he?
In terms of anime I think the previous poster might have thought of Rose of Versailles?
Also UK not US but I once saw a really weird and disturbing Dutch Alice in Wonderland.