[Buckeyephan]

The Prayer - Celine Dion/Andrea Bocelli and many others

[fdpaq0580]

Der Kommissar and the German version of Rock me, Amadeus. Sung by Falco

[Scorpyo]

Cuando Calienta el Sol. Sung by Vikki Carr, Connie Frances. Englebert, Ray Charles singers, Trini Lopez and more. The exact same music as Love Me With All Your Heart but completely different lyrics. I liked it so much I learned to sing it in Spanish.

[MacScuba]

Hips don’t lie

[bragones]

Una Paloma Blanca
Domo Arigato Mr Roboto
Psyco Killer

[MacScuba]

Rico Suave‘ – Gerardo

[Barryb46]

Originally Posted by LI SNOWBIRD

I'll start
The Singing Nun - Dominique https://youtu.be/EO7cD6qmydo

Cae SeraSera - Doris Day

[OrangeBlossomBaby]

Ma cherie amor - Stevie Wonder
this one is famous in English, but the original was (and still is) a Russian Folksong. I grew up hearing the Russian, before I ever learned to talk:

Theodore Bikel & Geula Gill - Dorogoy Dalnoyu (Russian Folksong) - YouTube

[coppadad]

Seaman by Lolita
Lolita - Sailor, Your Home Is The Sea (U.S. hit version 1960) - YouTube

[EnglishJW]

There are many wonderful songs in other languages that are used by dancers - all different types of dancers. Here is but one - a rumba or bolero. Son By Four - Donde esta tu amor ♥ - YouTube

[fdpaq0580]

(Hope I get close on the spelling)
Les Bicycklettes du Belsize by Mireille Mathieu

[EnglishJW]

Here is an older one most of us are likely to remember: Astrud Gilberto-One note samba - YouTube

[fdpaq0580]

Written in 1924 and sung by Sofie Tucker, Tom Jones and lots, lots more in many languages. My Yiddisha Mame.
There's an oldie for ya.

[Michael A. David]

By Wayne Newton.

[fdpaq0580]

Originally Posted by LiverpoolWalrus

I thought I read "...that are entirely not in English." And the example OP started with was a song entirely in French.

Hmmm. Now that I think of it, it could be ambiguous. Songs that are entirely not in English to me means the whole song is not in English. But if it's interpreted as "songs that are not entirely in English," then Ma Belle Amie and songs like OBB's In Your Eyes are valid. But for what it's worth, the question was phrased "entirely not in English."

Perhaps OP will clarify.

However you interpret it, got to admit it is a fun mental game. Reaching back into the shadowy, cobwebs filled corners of the mind to hunt down long un-remembered musical treasures from your past that celebrate different cultures is, in my opinion, fun.
Thanks to LI Snowbird for getting us started.