I jointly own a property with my brother, which we occupy in turns during the holidays. He wants to rent out this jointly owned house, but I do not. Does he have the right to do so?

No, not without your agreement. Renting out jointly owned property is an act of administration requiring the agreement of co-owners representing at least two-thirds of the undivided ownership rights (French Civil Code, Art. 815-3, para. 4).