ABBA and the Scorpions have been cited by many others, and were the first two bands I thought of. So I won’t dwell any further regarding them.
“Jerk it Out” by the Caesars:
The late Adam Schlesinger of Fountains of Wayne was in another pop band called Ivy, whose lead singer (Dominique Durand) is from France. Her accent is quite evident on many of their songs. “The Edge of the Ocean” was used in a number of movies (e.g., Angel Eyes, Music and Lyrics, Shallow Hal) and TV shows.
The Cardigans (Sweden) are pretty well known in the USA with several hit singles. My favorite is “Erase/Rewind”:
Lara Fabian. Her English-language hits are I Will Love Again and Love By Grace, but I’m crazy about her entire eponymous debut album. She’s Belgian, and like Celine Dion, her career began in French-language music, but for some reason, her attempt to cross over into the English-language market was not nearly as successful.
I really dig the Japanese bands that sing mostly nonsense English lyrics just because they like the way they sound and rhyme. I started my trip down that rabbit hole back in the early Eighties with The Plastics