Here's a list of non-English musicals I've seen submitted to @dyk-this-musical-song and links for how to watch/listen to them with English subtitles or the best equivalent. There are a bunch of non-English shows that have been submitted and seemingly some interest in checking them out, but I think a lot of people just have no idea how to go about that, or if it's possible. Disclaimer: I haven't watched these links, or if I have, it's been years, so possibly songs are out of order in playlists or shows are just linking to the first act. If that's the case, let me know and I'll make a note. A lot of these are pro-shots, which is fun. I listed shows here that have been submitted to the dye-tms blog, because that's a good way to gauge which have a decent amount of interest, but please let me know any you'd like added to the list.
Of all the ones I've checked out already on here (Tanz, Elizabeth, Marie Antoinette, Rebecca, Mozart l'Opera Rock, Kristina), Elisabeth is by far my favourite and probably the most popular internationally. It's historical but with heavy Phantom of the Opera vibes, if you're into that. But it's a good place to start, maybe.
Also there are a decent number of musical movies in non-English languages, often with English subtitles. I haven't included anything that exists more as a movie than as a stage show; this is more about stage shows, but a musical is a musical. To list the two I can think of, there's Les Paraplouies Des Cherbourg (The Umbrellas of Cherbourg) and Les Demoiselles de Rochefort (The Young Women of Rochefort), both in French.
Friedrich: Mythos und Tragödie (Friedrich: Myth and Tragedies) (German) there’s just the German album and you can follow along with the Wikipedia summary if you want , but this lovely person made a post about subtitles they made
Tanz der Vampire (Dance of the Vampires) (German) Here
Elisabeth das Musical (German) Here; there are actually multiple German-language productions with English subtitles, since this show is so popular. If you want, you can also find English subtitles on productions in several other languages (mostly, Japanese and Korean). I picked this one randomly, hopefully it's a decent enough video and isn't missing any critical scenes, if it's an early version.
Rebecca (German) Here; there might also be English-language videos/audios out there, this did get a few performances in English, but it's been a whole Thing and is mostly put on outside of English-speaking regions.
Mozart! Das Musical (German) Here
Marie Antoinette (German) This is just act 1, not act 2. I can’t remember if it’s sung-through or not. I can't find any translations of act 2.
Artur--Excalibur (German) Here So this premiered in Switzerland but it's written by Wildhorn, so originally was more an English show, but I don't believe has ever been performed in English. There are a few shows like this, Wildhorn is weirdly popular abroad as compared to in the English-speaking world.
Robin Des Bois (Robin Hood) (French) This has Russian open captions and closed captions, so you could use auto-translate on the closed captions, but it would be hard to read them with the open captions behind that so maybe set the subtitle background to opaque.
Le Rouge et le Noir (The Red and the Black) (French) Here
Notre Dame de Paris (French) This is actually an English version; here is a French-language one with English subtitles
Roméo et Juliette, de la Haine à l'Amour (Romeo and Juliet: from Hate to Love) (French) Here
Le Roi Soleil (The Sun King) (French) Here
Mozart l'Opera Rock (Mozart: the Rock Opera) (French) Here
Anne de Bretagne (Anne of Brittany) (French) I couldn't find any translations but here's a proshot
1789: Les Amants de la Bastille (1789: the Lovers of the Bastille) (French) Here
Adam et Ève: La Seconde Chance (Adam and Eve: the Second Chance) (French) Here
Dracula: Entre L'amour et la Mort (Dracula: Between Love and Death) (French) Here is a version with Russian and Serbian subtitles that you can auto-translate to English; here is the same video but with fan-translated English subtitles
Dracula: L'Amour Plus Fort Que la Mort (Dracula: A Love Stronger than Death) (French) Here is a version with Spanish subtitles you can auto-translate to English
La Légende du Roi Arthur (The Legend of King Arthur) (French) Here
A Dzsungel Könyve (The Jungle Book) (Hungarian) I don’t think there’s anything besides the Hungarian-language album, so try that and the wikipedia summary and maybe that’ll work.
István, a király (Steven the King) (Hungarian) Here, also here
A padlás (The Attic) (Hungarian) Here
Jónás Könyve (Book of Jonah) (Hungarian) Here
Valahol Európában (Somewhere in Europe) (Hungarian) translations of lyrics are here; I'm not sure if those are of all the songs. Here is the show in Hungarian.
A Pál utcai fiúk (Paul St. Boys) (Hungarian) Here is a playlist with some videos of songs and those are translated, the rest are from the cast recording and are not. I'm not sure if the playlist is in the proper order or not.
1989 (Polish) Google drive link to a video with subtitles; made by @perplexingly; thank you so so much!!!
Mieszko Pierwszy (Mieszko the First) (Polish) Here
Kristina från Duvemåla (Kristina from Duvemåla) (Swedish) Supposedly there is a movie but idk if it’s subtitled; there is an English-language translated version of the album and it’s sung-through; that’s available on YouTube
데스노트 (Death Note) (Korean) (there is an English version of this show; I’m not sure if it’s significantly changed or if it’s just a direct translation, but you can watch that) japanese production from 2017 korean production from 2015
프랑켄슈타인 (Frankenstein) (Korean) on Disney Plus, if you use a VPN to claim you're in Korea, but English subtitles probably aren't available.
Xcalibur (Korean) on Disney Plus, if you use a VPN to claim you're in Korea, but English subtitles probably aren't available.
Doornroosje (Sleeping Beauty) (Dutch) no translations filmed show, no subtitles, Dutch album, no subtitles
Tarzan (Dutch) Dutch album, English version of the album Scenes are missing from both; the English Broadway production can fill in those gaps
Soldaat van Oranje (Soldier of Orange) (Dutch) no translations I could find; here’s the album
3 Musketiers (3 Muskiteers) (Dutch) Here
Демон Онегина (Demon Onegin) (Russian) Here
Последнее испытание/ПредПоследнее Испытание (The Last Trial) (Russian) Here is the movie; here is a proshot
Мастер и Маргарита (The Master and Margarita) (Russian) Here is a version with Russian subtitles that you can auto-translate to English