French quadruple turret tradeoffs

Why were the French putting quadruple turrets on battleships when there was no treaty yet?

Quadruple turrets improve tonnage efficiency and density of fire, but they create serious operating and beam problems.

Quadruple turrets promise more firepower for less turret weight, which made them attractive even outside a simple treaty explanation. Comparing quadruple, triple, and double arrangements shows how quickly turret weight adds up. Four guns in one turret, however, demand beam and operating complexity that can make the lighter arrangement difficult to use.