Would French rearmament trigger a wider naval race?

Would France's response provoke Italy, then Britain, Japan, and the United States into a larger naval race?

Only partly; several navies are already at industrial or political limits, while Britain can respond by accelerating existing orders rather than creating a new program.

The reaction chain stops where political and industrial capacity runs out. France can accelerate Joffre, but Italy is already straining to complete the Littorio class and an Italian carrier would reopen the struggle between the Regia Marina and Regia Aeronautica. Britain mostly speeds ships already planned rather than announcing a wholly new fleet, reducing the signal that might provoke the United States. Japan is likewise near the limits imposed by its Yamato-class program, so the scenario produces uneven acceleration rather than an automatic global building spiral.