Would France have left the treaty over Caracciolo?

Would France have walked out of the Washington negotiations if Italy demanded the right to complete Francesco Caracciolo?

Probably not. Italy had precedents among the other powers, while France had strong financial and security reasons to remain in the treaty system.

Italy had a plausible precedent for completing one modern hull because the United States and Japan were completing ships while Britain received two new capital ships. France would also have weakened its own position by walking away from a system backed by British and American financial and security influence. The French delegation would probably have sought a bargain, even one unfavorable to France, rather than collapse the conference over the Italian request. This makes a French walkout an unlikely response to completing Francesco Caracciolo.