Hi!
Here your legal rights:
Peut-on contester un permis de construire accordé à un voisin, et si oui, comment ? - Service-public.fr
Please note the possible delay: 2 months after posting on the Mairie board.
but if the Maire is against it, ask him for details of what he is doing - What other supports he may have. Is it possible to act together?
Yours,
giantpanda