Here’s the Johnny Horton song, Sink the Bismarck.
It’s an American country-western song, but it’s extolling a British victory in WWII.
Are there other songs that praise another country’s military wins, or another country’s anything come to that?
Well, there probably are some that praise foreign women, but other than that.
Well, IIRC, he was hired to do that song for the film’s ad campaign.
It was inspired by the 1960 British war movie Sink the Bismarck! and was in fact (with the producer John Brabourne’s approval) commissioned from Johnny Horton by 20th Century Fox who were worried about the subject’s relative obscurity in the United States. For some reason the size comparisons of guns and shells are switched. While the song was used in U.S. theater trailers for the film, it was not used in the film itself.
Praising foreign women is easy.
Remember, the movie title had an exclamation point after it. More movies should do that!
West Side Story!
Forrest Gump!
Dune!
House of Gucci!
Licorice Pizza!
63 Up!
The Eyes of Tammy Faye!
Pretty much the entire output of Swedish heavy metal band Sabaton is praising other countries’ military exploits.
Now you’re oozing into Clive Cussler territory – I have no idea why so many of his novels have ! in the titles:
Raise the Titanic! (-- I’ll let that one slide)
Vixen 03! – ??
Several others!!
It sells books, that’s why!
There should be a “Sink the Bismarck! Then Raise Her, and Sink Her Again!”
Another ‘Dirk Pitt’ adventure??!!!?! 
Oddity or not, Sink the Bismarck! is a snappy tune about a historical event. Johnny Horton specialized in them. The Battle of New Orleans, North to Alaska. Why can’t we have more snappy historical songs?
There are various songs in Stop the World I Want to Get Off extoling women of several countries. Here’s an example:
Indeed, after The Battle of New Orleans, Horton was the go-to guy for songs about historic battles. If not for his untimely death, I don’t doubt Horton would have ended up recording P.T. 109 instead of Jimmy Dean.
Are there other songs that praise another country’s military wins
How about the 1812 Overture?
Well no, Tchaikovsky was Russian after all.
By a Russian composer, celebrating a Russian victory. So, no.
Does Black Country Communion count as an American band? It was formed in the United States and two of its four members were Americans. (The other two were English.)
If so, their song The Battle for Hadrian’s Wall is a song about a battle that doesn’t involve any Americans.
As God is my witness, I thought Napoleon won the Battle of Moscow. 
Well Moscow did burn down.
Although it’s a completely fictional battle, which may not be what the OP had in mind.
The Irish traditional repertoire includes a couple of songs celebrating the French victory at Fontenoy over a combined force including British, Dutch and Imperial troops in 1745. The Irish connection to the battle is that the French forces included the Irish Brigade, a unit of the French army made up of exiled Irish soldiers or, by 1745, their descendants. This was a French victory, though, not an Irish one.