The maths teacher and the 14-year-old student, who was in his class last year, began chatting on Instagram on February before beginning a relationship in June.
Her parents accuse the teacher of being a sexual predator, despite their daughter's claim that the pair are in love.
"She's a child who believes in love with a capital L. As a teacher he knew that and used it to seduce my daughter," her mother told the AFP news agency.
There is no minimum age of consent in France, which does not treat sex between an adult and a minor as rape unless there is proof of force.
President Emmanuel Macron has promised to change the law after a man was acquitted of rape earlier this month, as the jury found no evidence he had forced an 11-year-old girl into sex.
Currently sex with a minor aged under 15 is classified as sexual assault, punishable by up to five years in prison.
Adults wielding some form of authority over the child face tougher sentences.