The 35-year-old actor is said to be head over heels for the 26-year-old actress and has been telling friends she is the one for him, reported Contactmusic.
"James is in love. He says Emilia is the most amazing woman he's ever met," a source said.
The couple were spotted at an art fair in New York last month, where Franco could not keep his hands off Clarke.
In 2011, Franco had split from his long-term girlfriend Ahna O'Reilly after dating for five years.