Godrèche, 51, accused Jacquot, 77, of raping her in 1986, when she was 14, and of a relationship she "forcibly" maintained until the 1990s.
Jacquot said he "unequivocally" denied the allegations and accusations.
Godrèche became known early in her career for her roles in two of the director's films, The Beggars (1987) and The Disenchanted (1990). She recently spoke anonymously about her relationship with Benoît Jacquot on the autobiographical TV program Icons of French Cinema.
She recently named Jacquot on social media, saying she decided to do so after watching a documentary about the director's relationship with a teenager in 2011. In an interview with Le Monde newspaper, Jacquot said he "flatly denies Judith Godrèche's allegations and accusations".
Reached by AFP on Wednesday, Jacquot said he stood by his remarks and did not wish to speak further.
Godrèche's complaint was filed with the Child Protection Brigade in Paris, lawyer Laure Heinich told AFP.
