Godreche took to social media in January to accuse Jacquot, now 77, of luring her into a relationship by posing as a vulnerable underage actress.
Le Monde said the crime was punishable by up to 20 years in prison, although the statute of limitations in the case had “probably” expired.
The relationship began in the spring of 1986, when Godreche was 14, and ended in the early 1990s.
Godreche said she remained “in his grasp” for six years, starring in two films directed by him, ‘Les Mendiants’ (The Beggars) in 1988 and ‘La Désenchantie (The Disenchanted)’ in 1990.
When she learned in a 2011 documentary that he was describing his relationship as a “crime” and that cinema was providing “cover” for it, he decided to rant about it.
Director Jacquot, who has made more than 50 films and TV movies, has said that he needs to “fall in love” with his actresses before filming.
She has worked with established stars such as Catherine Deneuve and Isabelle Huppert as teenagers, as well as Godrecht, Virginie Ledoyen and Isilde Le Besco.