Welcome to my French pop and rock section... Here are a few recommendations to albums I've enjoyed that I think you might like as well, ranging from 1960s ye-ye to a few more contemporary albums from France's blossoming indie and electronica scenes. There is also a separate section for older musical styles, such as chanson and musette, if you like the old stuff, too!
Tiny Yong "L' Integrale: 1961-1965" (Magic, 1998)
A protege of Henri Salvador, singer Tiny Yong was born in Cambodia and first made her name singing in cabarets and on film. She went "ye-ye" in the early '60s, and this disc holds the results. It's pretty good, actually!
Zazie "Zest Of Zazie" (Mercury-France, 2008)
Murky, languid, often bland, synth-bubblegum-pop -- sort of a trip-hoppy French version of Kate Bush, with a bit of Siouxie & The Banshees in there as well... Though those comparisons probably make Zazie sound more interesting than she actually is; this is easygoing Europop with a teensie bit of a 21st Century facelift. Zazie has a bunch of albums, dating back to the early 1990s, but they're all a bit too mainstream for my tastes... This best-of disc is probably enough to satisfy most people's curiosity.
French Music Index
French Chanson & Musette