Or Bobby Vinton’s “My Melody of Love,” sung partly in Polish.
No, I will not let you all forget…
Rico Suave
O-Zone “Dragostea Din Tei” – better known as the Numa Numa Song.
We No Speak Americano. Despite the spanglish (ital-glish?) title, it’s almost totally in Italian, as it’s a recent remix of a 1950s Italian hit, Tu Vuò Fà L’Americano.
The 45 RPM record I bought at the time had both versions, one on each side. (I don’t remember which was “A” and which was “B” though.)
And to fit in with astorian’s reporting, I remember the German version getting more air play.
Soul Makossa by Manu Dbango.
Is the OP concerned only with songs which are entirely non-English? Because there are lots of pop music hits which are partly or primarily in English with some verses or the chorus in a foreign language. “Suite: Judy Blue Eyes” by Crosby, Stills & Nash comes to mind – as its name suggests, it’s a suite of four parts, with the final part sung in Spanish; it charted at #21 on the Billboard Hot 100. If even briefer foreign-language sections are permitted, then I could submit Beck’s “Loser”: the first line of the chorus is in Spanish, and there’s some German chatter at the end. The song got to #10 on the same chart.
“Vera Cruz” and “Hula Hula Boys” by Warren Zevon meet that criteria, as does “Psycho Killer” by Talking Heads. (Spanish, Hawaiian, and French, respectively)
“You Were the One” by Billy Joel is about half French.
Michelle - The Beatles
Maybe it stopped at that position at some point during its chart lifespan, but its actual peak position in Billboard (which is the chart mentioned in Wiki, using a NY Times article as a source) was #58. The album containing the song did also include a track called “69 Année Erotique (69 The Erotic Year).”
*The Witch Doctor *(partially in English):
“Oo ee, oo ah ah
Ting tang walla walla, bing bang
Oo ee, oo ah ah
Ting tang walla walla, bing bang.”
And *Mairzy Doats *(quasi-English):
“Mairzy doats and dozy doats
And liddle lamzy divey.
A kiddley divey too,
Wouldn’t you?”
And the Beatles did (among others) *She Loves You *and I Want to Hold Your Hand in German.
Worth a mention is Pink Martini, an American ensemble that frequently performs in other languages. I’m not sure they ever charted in the US, but songs like “Sympathique” and “Dond’estas Yolanda” got some serious chart action abroad, and were sung in French and Spanish, respectively.
I’d forgotten this, but back in 1975, the Captain and Tennille had a huge hit with Neil Sedaka’s “Love Will Keep Us Together.” After it became a hit, Toni Tennille went back to the studio and re-recorded her vocals in Spanish.
The song was re-released under the title “Por Amor Viviremos,” and reached #49 on the Billboard charts.
It looks like Chanson D’Amour charted 3 different times by different artists. (rrra-tata-tata)
I’d never heard of it until it was covered on Are You Being Served? 
Although it doesn’t quite qualify, Prisencolinensinainciusol deserves an honorable mention.
“Sunday Girl” by Blondie (and, I think, also their “Denis, Denis”) has a verse in French.
In Britain, Steeleye Span had an Xmas hit with “Gaudete,” which was sung completely in Latin, and a capella.
So does Lady Gaga’s “Bad Romance”. 
Electric Light Orchestra’s “Hold on Tight to Your Dreams” has a verse in French.