Excluding some that have already been mentioned, I think the first one I saw in a theater with the subtitles was The Tall Blonde Man with One Black Shoe, which later had a Tom Hanks American version as The Man with One Red Shoe. Very funny, even reading subtitles.
I made sure to eventually see the sequel, The Return of the Tall Blond Man with One Black Shoe.
I think the category should be first foreign language film, otherwise Porkey’s or James Bond movies would count.
The first subtitled movie I can remember seeing in the theater was Das Boot.
I saw Night and Fog at school, somewhere in junior high.
For foreign films that I willingly went to see in an actual movie theater: In 1985, I had a crush on a guy who saw a lot of films at the local art house theater, the obvious result being that I started seeing a lot of films in that theater. The earliest I can figure is Zuckerbaby, a German movie … for years, I would have said it was Mishima, but apparently that’s not a foreign film. That gives a good sense of the time frame, though.
8½.
I was about 14 and I’m sure it went right over my head. I suspect it would still go right over my head.
Sounds very familiar - the difference was that I saw Das Boot as the TV mini-series, although I was aware that it was a film as well. If that doesn’t count, then it was Jean de Florette.
Swedish Erotica?
Actually it was Das Boot.
While there might have been something when I was in high school that I don’t remember, I saw Solaris in college. I went WTF then. A few years later I saw it with my ex who is Russian and I was still WTF. Then I saw the Clooney verison and I’m still WTF. I’ve also read the book. I think I must be hopeless.
The Red Balloon - I think every grammar school in America has shown this.
The first one I watched by choice might have been Two Women. Or La Dolce Vita.
The first movie I recall seeing was Indiana Jones and the Temple of Doom, dubbed into Russian. I was three, and the fiery pit scared the shit out of me for a good week.
The first non-US film I saw after coming here was probably The White Sun of the Desert, which is the Russian equivalent of a Western set in the civil war of the early 20s. Very much worth seeing if a subtitled release exists.
I’m glad you phrased the OP the way you did, because, though we are a minority, there are still about a hundred regulars (guesstimate) who post regularly and who don’t have English as a first language.
First time to a theatre, and my first time exposure to a feature length, animated movie - Jungle Book. With hindsight, it’s far from the best Disney feature, but it’s my favourite.
Red Balloon (natch)
But then Allegro non Troppo, which included black and white (barely) comic interludes with lime green subtitles. 
Jules et Jim. On public TV when I was about 7. Bored me stiff.
I got to see it again in my 30s. Result: about the same.
The first one that really made an impression on me was M. I still am suffused with awe when I watch it.
The first movie I saw cognizant of it being “foreign” was Bertrand Tavernier’s Round Midnight, which is now my favorite movie of all time. IMDb says it’s “USA/France,” but I think a French director and a French star should count. So there.
Seven Samurai.
Edit: Also the first black & white film I saw.
I think it was Akira.
Betty Blue. 
Not entirely sure. Our local PBS station, when I was a kid, showed a series of foreign films(non-English speaking that is), and I remember seeing Rashomon, The Battleship Potemkin, and Alexander Nevsky. The dialogue of the latter was kind of klunky, but the music was amazing. In Battleship, which is a silent film, the action was so intense(remember the soldiers marching down the Odessa steps?), that I can “remember” sounds of screaming, although of course there wasn’t any. And Rashomon marked the first film in which I saw Toshiro Mifune*, although I didn’t really know anything about him for years.
**Throne of Blood * was a great film, possibly the best “Macbeth” I’ve seen.
Last Year at Marienbad. 1961. I was blown away.
As a rather sheltered, naive, conservatively raised kid of the 1940’s-1950s, subtitles seemed weird. But nothing you couldn’t overcome.
I blame this for all of my current problems.
After the usual Saturday morning cartoons were over, on CBS (in keeping with its “Tiffany Network” cred) ran “The CBC Children’s Film Festival” (aka"Kukla, Fran and Olie.") It was a showcase for foreign children’s movies.
I recall watching a Polish movie about a artist’s apprentice in the middle ages who is given a pair of yellow slippers by a princess, and a Soviet films about a lonely game warden who befriends a wildcat; a bunch of Russian kids in red neckerchiefs who sprayed each other with red paint and played Indians; and O’Henry’s “Ransom of Red Chief,” which was well-served by the expansive gestures typical of Russian acting.
But it wasn’t all Commie agitprop. One of my favorite movies was a B&W English one about a little Catholic boy who makes friends with a little Jewish girl. After they resolve his chagrin at her being a Christ-killer, they decide to take a liferaft to Africa and nearly drown. I remember Findlay Curie selling the boy a pith helmet, which struck me bcause I was the only kid I knew in real life who had one.
Nobody else watched “Kula, Fran & Ollie.” When it came on that was the signal cartoons were over and it was time to get outside.
Renoir’s “Rules of the Game,” on TV, when I was, maybe, ten? Anyway, just barely old enough to figure out what was going on, but old enough to know that the film was of a class better than what I was used to seeing. Later (as an adult), saw “Diva,” and, of course the obligatory “The Red Balloon.”