I’ve been really into K-pop recently (see my signature) so I’m aware that several K-pop songs have got onto the Billboard charts recently, especially from the massively popular boy band BTS. (They recently sold out Citi Field in New York in 20 minutes, something no other Korean band has come close to accomplishing, and hardly any western band can do.) Wikipedia has a list. All the songs listed are K-pop, though a few are English versions, as shown.
Dang it! Kraftwerks’ Numbers missed the non-English mark by “One Two” words.
From the OP:
But acceptable, per my opening post.
Guantanamera, The Sandpipers
Volare (Nel blu dipinto di blu), Domenico Modugno. It was also charted by Dean Martin and Bobby Rydell in combinations of Italian and English.
What about the ersatz German to kick off Def Leppard’s “Rock of Ages”? 
(Or sampled somewhat more recently in Offspring’s “Pretty Fly for a White Guy.”)
The day I read the OP with any understanding is the day I. . . um, stop making a fool of myself!
Does Tequila count?
The same sort of nonsensical “German” kicked off Snoopy vs The Red Baron, by The Royal Guardsmen.
ELO’s, “Hold on Tight,” has a verse in French that is (I think) a reprise of the first verse.
The Beatles, “Sun King,” has some kind of different language at the end 
.
The Clash translating a verse into Spanish in Should I Stay or Should I Go is one of my favorite Spanglish moments in pop.
Or Beck’s Loser – “Soy un perdidor…” (not really how you’d say “I’m a loser” in Spanish).
Likewise April Wine’s “Just Between You and Me.” Eh, they’re Canadian.
The summer of '69 was full of Romance-language shenanigans…see CSN’s “Suite: Judy Blue Eyes” (Stephen Stills did spend part of his childhood in Costa Rica, so his attempts are a little more serious than Lennon’s).
And R.E.M.'s 1986 cover of “Superman” starts with a Japanese pull-string Godzilla doll’s talking.
If you’re gonna count fake foreign languages, The Witch Doctor was a pretty big hit.
Also Sheb Wooley’s (as Ben Colder) “Don’t Go Near The Eskimos”, a parody song starting with some fake Inuit lyrics that somehow made it to #18 on the country chart.
Back to business:
Pata Pata, Miriam Makeba, charted at #12 in the US. This was sung in her native Xhosa “click” language.
David (Bread) Gates had a hit with, “Took the Last Train,” which has its chorus in French and then repeated in English.
Ray Stevens’, “Ahab the Arab,” has some mock-Arabic in it (and Camel-speak by Clyde).
“The Girl from Ipanema” has been mentioned. I thought sure there would be a lot more bossa nova and samba songs that qualify, but I could find only one more that both charted on the Billboard Hot 100 and has lyrics in Portuguese.
“Mas Que Nada” by Sergio Mendes and Brasil '66 hit #47 on the Billboard Hot 100 chart in 1966
I always thought the parody version, 99 Words for Boobs, should have received more recognition. Who needs words in any language, anyway? (NSFW)
Edith Piaf’s “Milord” with lyrics in French somehow managed to hit #88 in 1961. It’s far from her best effort.
Claudine Longet’s version of “L’Amour est Bleu” with the original French lyrics and a few spoken words in English hit #71 in 1968. The original version by Vicky [Leandros] seems not to have charted in the US. Several other artists also charted with their own versions of the song, but I think they were all either instrumentals or English translations.
I’m getting my data on peak chart position from Hot 100 Singles Chronology.