The 40 year old was spotted enjoying a cosy break with Biolay on the French island of Corsica earlier this month (Dec13).
A source tells the New York Post's Page Six column, "They clearly wanted to be alone. They spent all their time at the hotel, moving only with three bodyguards and in a car with heavily tinted windows."
The pair was allegedly introduced to one another by Chanel design icon Karl Lagerfeld, who counts Paradis as one of his fashion muses.
Paradis' 14-year relationship with Depp broke down last year (12) and the Hollywood hunk has since gone public with his new girlfriend, his The Rum Diary co-star Amber Heard. The former couple shares two children together - daughter Lily-Rose, 14, and son Jack, 11.
Biolay was previously falsely linked to France's former First Lady Carla Bruni, and he was awarded damages over the affair allegations from Tv network bosses in 2010.