Exception: if your rental contract had insurance included (with deductible, since you are charged for minor damage), do not submit any claims to credit card: you will lose time, and it will be denied, while you will have agreed that there was a damage on your rental.

If French Hertz does not reverse the transaction, you already have a proof from correspondence with Hertz that there was no damage and shouldn’t be any charges. Submit that pdf with disputing the charge to the credit card