Bruni, who is pregnant with her second child, is said to have forged a close relationship with the Libertines star over their shared love of poetry and music.
It is thought that Doherty, 32, and Bruni were introduced in Paris, just days after his early release from jail for cocaine possession.
The 43 year-old will reportedly even attend one of Doherty's concerts in France later this month.
A source told British newspaper the Sunday Mirror: 'They've met up several times and really hit it off. Pete really enjoys Carla's company and is flattered by the fact she wants to spend time with him.
'Carla is just the type of woman Pete likes - intelligent, sophisticated and extremely beautiful.'
The source added: 'She knew all about his music and career, and he was, of course, flattered.'