The Russian version of Finding Dory has a song "Дари Дори" ("Dari Dori") written and performed by a band FRUKTЫ (Fruits) playing during the closing credits in place of "Three Hearts", "Loon Tune" and "Fish Who Wander." When the song ends, the beginning of "Three Hearts" can be heard, slowly followed by the ending part of "Release."
How to Train Your Dragon 2 has Into a Fantasy in the Norwegian dub, performed by Hiccup's Norwegian voice-actor Alexander Rybak. Perhaps more a case of an "Additional Foreign Theme Song" though, as the original theme Where No One Goes is also kept in the dub, with this song playing after it in the end credits.
The French dub of The Lion King 1 ½ replaces the song "Grazing in the Grass" and the reprisal of "That's All I Need" with "Can You Feel the Love Tonight" by Star Academy 3. See here.
The theme of the Latin American version of Open SeasonTu Eres El Amor by Reyli (who also did the voice of Boog in that version).
The European version for Tarzan has the song "Son of Man" play instead of "You'll Be In My Heart" for the start of the credits.
The British release of Toy Story does this by replacing the instrumental songs from the end credits with a variant of "You've Got a Friend in Me."
Similarly on the British release of Toy Story 2, over the end credits it replaces Wheeze's version of "You've Got A Friend In Me" with an instrumental version Of "Woody's Roundup."
The British version of Monsters, Inc. does this as well.
"Witaj w moim swiecie" by Edyta Bartosiewicz is the ending theme for the Polish version of Winnie the Pooh (2011). This song was also used (and translated) in the Ukrainian, Hungarian, Bulgarian and Romanian versions of this movie.
In Swedish, All Dogs Go to Heaven's theme song is "Änglahund", sung by renowned Swedish singer, Hasse Andersson (albeit a rerecording of the original 1982 song.)
Certain dubs of Hercules, including Swedish (excluding the DVD release), Norwegian, Finnish, Russian and Icelandic, replace the reprise of "A Star Is Born" in the credits with Belinda Carlisle's cover of "I Won't Say I'm In Love".
Most of the music used in the French dub of The Magic Roundabout 2005 film adaptation is unique in several scenes, since the English dubs (as well as other foreign-language versions of the film) used more insert pop songs. For example:
A different lyrical song is used during a dream sequence, as opposed to the Electric Light Orchestra song "Mr. Blue Sky" used in the English versions.
The title song performed at the end of the film and through the end credits in the English versions, is moved to the opening credits in the French dub, while another different lyrical song is performed at the end of the film (the opening credits in the English dubs use the Pilot song "Magic").
Lapitch The Little Shoemaker has an inverted case applying to both the main theme and all the songs throughout the movie; though the movie's different dubs including English generally share the same tunes (with the main theme being the basis for the TV series' intro), the Croatian dub has entirely different musical numbers while also being the original version.
While most Dingo Pictures dubs retain the original songs, sometimes leaving the lyrics in German, the French dub of Wabuu has a completely new theme tune.
The Hunchback of Notre Dame has a variation, American prints Closed with Music/All-4-One's version of Someday, whilst British prints instead used Music/Eternal's Version.
A similar thing occurred with Mulan, where the American version had Music/Christina Aguilera's version of Reflection and the British version had Vanessa Mae's version.
Other
Spanish-made superhero B-movie Supersonic Man: Where the English language prints got a low-budget attempt at a superhero fanfare, the original Spanish release got a funky Euro-Disco song.
The Twilight Saga: New Moon features different themes depending on the release country or foreign language dub. The Japanese theme, "Destiny" is already covered on the Asian Releases subpage, but here are the others:
The Australian version has "Thunderclap" by Eskimo Joe.
In Spanish, it's "Sed" by No Way Out. The Mexican version also has an additional theme in the form of "Frente al Mar" by Ximena Sariñana
In French, it's "Cavalier Noir" by BB Brunes.
In German, it's "Es Tut Wieder Weh" by Jennifer Rostock.
(the film title in French).
