"fast enough to hunt down, and kill other cruisers" The 'other cruisers' were the 32-33knot 10,000ton 8in gun Washington Treaty cruisers.
France had an allowance of 35,000tons to replace earlier capital ships in 1927, so could build two of these small battlecruisers then.
Sorry to contradict you but, France and Italy were allowed to replace two old battleships each for a total of 70,000 tons per country. France could build four 17,500 ton battlecruisers. Each of these designs are multiples of 70,000 tons. The next design is for a 23,690 ton Battlecruiser. Stay tuned.