That's a great idea for a legend like Charles Aznavour ! Actually, learning foreign songs might be my favorite way to learn languages
There are probably more, but three songs pop into my mind right now:
1) Own Yourself - Nâaman (English / French): I don't know if it can be considered bilingual, since the whole song is in English and there is only the last verse in French, but I really like that song. Nâaman is French but he mostly sings in English in his songs, and that's one of the rare ones where he sings a bit in French ^^
https://www.youtube.com/watch?v=ZH9NyHSrQ7Q
2) Liberta - Pep's (French / English): This time only the chorus is in English, and the rest is in French.
https://www.youtube.com/watch?v=Nx7cT6dP5Xk
3) Je réalise _ Sinik (feat. James Blunt) (French / English)
https://www.youtube.com/watch?v=vy-313FF7u0