The Awakening (2009)

In pouring rain, Dr. Voline, a night doctor, knocks down a naked young woman with his 4x4. Transported to the hospital, she doesn't remember anything and is declared carrier of an unknown bacterium. Refusing to be separated from the man who hit her, the unknown will prove to be a real enigma for Yann. In particular, he discovers in her strange powers allowing her to read thoughts and to exchange personality, memories and skills with those she meets.