I have just obtained planning permission from the town hall. My neighbour is threatening to apply for its cancellation because my construction is very likely to cast a shadow over his garden. Does he have legal grounds to do so?

Yes. Anyone with a legitimate interest may apply to the court to have planning permission cancelled; to do so, they have two months from the first day on which notice of the planning permission is displayed on the land concerned (Art. R600-2 of the French Town Planning Code). However, the potential loss of sunlight will not necessarily be grounds for cancelling the planning permission if it fully complies with planning rules (permitted building heights, etc.). If the harm is recognised by a court, you may be required to pay him damages.