[LI SNOWBIRD]

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

[Marvic 1]

How about - La Bamba -
.......... I'm not a Sailor, I'm a Captain...

[Ecuadog]

Nel Blu, Dipinto di Blu

[New Englander]

Sukiyaki, sung by Kyu Sakamoto

Sukiyaki (Ue o Muite Arukou) - Kyu Sakamoto (English Translation and Lyrics) - YouTube

[LiverpoolWalrus]

Komm Gibb Mir Deine Hand / Sie Liebt Dich, the Beatles
Sukiyaki, Kyu Sakomoto
Pata Pata, Miriam Makeba

...come right to mind

[LiverpoolWalrus]

Then there's this gem, which wasn't released in the US, but was performed by a band that is/was huge in the US, and deserves special mention in my humble opinion:

Rolling Stones(italian version)As tears go by... - YouTube

[Jayhawk]

ma belle amie

Tee-Set

TEE-SET - MA BELLE AMIE - YouTube

[LiverpoolWalrus]

Originally Posted by Jayhawk

ma belle amie

Tee-Set

TEE-SET - MA BELLE AMIE - YouTube

If we're going to include songs partly in a foreign language like Ma Belle Amie, then I'll throw in the Beatles' Michelle

[LiverpoolWalrus]

99 Luftballoons, Nena

[OrangeBlossomBaby]

Some songs that weren't "entirely" not in English but were focused on something not in English

Michelle - the Beatles (French + English)
Kyrie Eleison - Mr. Mister (Latin + English)
Volare - Dean Martin (English + Italian)
In Your Eyes - Peter Gabriel (English + Wolof)
Mea Culpa - Enigma (French, English, and Latin)

[Jayhawk]

Originally Posted by LiverpoolWalrus

If we're going to include songs partly in a foreign language like Ma Belle Amie...........

That was the request, you know?

[LiverpoolWalrus]

Originally Posted by Jayhawk

That was the request, you know?

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.

[Marvic 1]

Originally Posted by Marvic 1

How about - La Bamba -
.......... I'm not a Sailor, I'm a Captain...

It's been 3 hours and I'm still humming La Bamba.......... ........... HELP!

[Buckeyephan]

Wooden Heart by Elvis
My Melody of Love by Bobby Vinton

[mamamia54]

Pepino the Italian Mouse - Lou Monte