The important factor isn't the French navy - it's
French Indochina. Japan occupied northern Vietnam from the Vichy government in September 1940, and basically got a free hand in Indochina in June 1941, both of which depend on a Vichy government being recognized as having authority over Indochina. The US responded to the first event with a scrap-metal embargo against Japan, and to the second with an oil embargo and a freeze on Japanese financial assets in the US; the second embargo was especially important in the run-up to war, as it forced Japan into a situation where it had to either try to back down in China (and face the wrath of the Kwantung Army and its sympathizers, who often used assassination as a political maneuver) or to somehow seize the resources it needed to continue to prosecute the war in China (leading to the OTL war in the Pacific, or at least a facsimile thereof).
Avoid the occupations of Indochina... and things get messy. The US may end up embargoing the Japanese anyway. Even if they don't, there will be a lot of pressure coming from Japanese commanders in China to get cut and keep cut the railway lines running from Hanoi to
Kunming and into
Guangxi. Still, it's possible (not likely, but possible) that Japan muddles on through the '40s fighting only in China.