Can my french public university require me to have a Google account

I work at a Dutch University and at my university students are not supposed to be required to create other accounts than the ones the university uses (unfortunately we are in the Microsoft ecosystem). Lecturers who design an assignment that requires a third party login must provide an alternative for students who refuse this. So I would recommed you to look into your university’s policy and file a complaint if this lecturer violated the policy. Or you could discuss it with your student council. They often know well how this can be addressed best.