This gas distributor comprises at least one elongate crosspiece including two side walls, inclined on their upper parts, connected to one another in their respective upper parts and defining a gas circulation housing between them emerging downward. The gas distributor includes at least one reinforcing member arranged in the housing defined in the elongate crosspiece, the reinforcing member including a central vertical plate that extends longitudinally in said housing and at least one bracket fastened transversely between the central vertical plate and the side wall of the elongate crosspiece.