Amazon reviewed her first album:

Originally best-known as an Italian-born model who had affairs with Mick Jagger and Eric Clapton, Bruni has matured into a remarkably talented and self-possessed singer-composer-guitarist. Her debut album, sung mostly in French, could best be described as neo-chanson. Bruni's whispery, wobbly, husky voice, wryly deadpan delivery and introspective lyrics recall Francoise Hardy, Barbara, Jane Birkin and Nico. But unlike her forebears, who so often posed as waif-like child-women and doormat-like victims of passion, Bruni remains firmly on top. Her lyrics can and do celebrate true love but she also praises the delights of female sexual empowerment in no uncertain terms, as on J'en Connais ("I've Known A Few"). Musically, the tunes range from folk Français to echoes of le jazz hot to bluesy torch numbers. The spare, mostly acoustic instrumentation is unfussy and atmospheric, while the I-couldn't-care-less ambience is occasionally punctuated by chimes, insouciant whistling or an impudent, sly giggle.

Here's All Music Guide:

Carla Bruni is an Italian supermodel and this is her first album. Like Milla Jovovich's debut, this caught everyone by surprise. It's a very good effort, far beyond what one would have expected. It's an acoustic and intimate album, and the songs are from her own harvest. She also plays guitar. The talented French guitarist Louis Bertignac produced the album. Although she's Italian, most of the album is sung in French with some Italian touches, like in "Le Ciel Dans une Chambre." The result is a kind and smooth album that mixes folk and chanson Française in equal parts. Although she's not breaking any new ground, the result is compelling.

Linked here is a live version, with concert video. You can also listen to the album version, for which there is no video.

Her new album, No Promises, is out now (in the US, via import).