Definition of floor manager
The expression is English-speaking. How often you will hear it will depend on the casino you are in. In French, it would probably mean the manager of the tournament room. The expression "appeler le floor manager" means "to call the management of the casino or gaming room". When you play indoor poker, you call floor (simply) or floor manager when you have a conflict. Usually, players can get along with each other. If they can't, the dealer will always be able to decide, but in really difficult situations, the floor manager will be called as the ultimate authority. The floor manager tries as much as possible to be fair and impartial.
An example where we can call the flop manager
You are on the river and an opponent is betting big. You are really hesitating; should you call the bet or fold. You're thinking about it. Suddenly you make a gesture that might make it look like you're putting your hand down. Instantly your opponent shows you a bluff. You let him know you haven't folded yet and call the bet. Your opponent disagrees and assures you that your hand was folded. Sometimes it can be hard to tell who is right. In such a situation, you call the floor manager.