PARIS — Just a 10-minute walk from Notre-Dame Cathedral, the bakers union headquarters looked like every other stone building on the Île Saint-Louis. But once through the enormous wooden red doorway, you knew you were in the right place.

On the ground floor, the smell of buttery pastries wafted from a test kitchen packed with students. There was flour everywhere. Sacks of it lined the hallways. Dusty white footprints marked the carpeted stairway to the judges’ chambers. And outside, you could spot the bakers — not students but bona fide professionals — by the flour on their clothes.