Do French double-twin turrets save weight?

Could two double-twin turrets be lighter than a three-by-three main-battery arrangement?

The answer rejects the proposed weight saving: the French double-twin mounting is not lighter than a triple turret.

The French arrangement places two twin-gun mechanisms inside one turret. A failure affecting one half can leave the other pair of guns working. The audience also raises the risk of a jam affecting the whole mounting. Dividing the mechanisms does not establish a weight saving over a triple turret, and the answer rejects the suggested advantage without supplying comparative weights.