I think if Japan takes FIC, that ends the $10 NO period. It doesn’t matter if France declared war on Japan or not. However, if France declared war on Japan, but Japan did NOT take FIC, then they can still get the $10 NO for peace with USA. Same thing goes if UK/ANZAC declares war on Japan first. As long as they are still not at war with USA and haven’t taken FIC, they still get the $10.
Japan collects $10 if:
Japan is not at war with the United States
Japan has not attacked French Indo-China
Japan has not made an unprovoked declaration of war against United Kingdom/ANZAC.
So you see, if UK/ANZAC declared war on Japan first, then any declaration of war by Japan would then be considered provoked and the $10 NO with the USA would still be in place.
Theoretically, Japan could collect this NO for more than 3 rounds. While it is generally regarded as only possible during the first 3 rounds while USA is still neutral, and while it is highly unlikely, the USA could remain neutral past round 3. The rules say that the United States MAY declare war on any and all Axis Powers during the Collect Income phase of round 3, the US doesn’t necessarily have to. OR, it’s also possible that USA only declares war on Germany and Italy. True, it would be a very weird scenario and almost guarantee an Axis victory, but it is technically possible. In this case, every round that USA and Japan are not at war with each other, as long as Japan never takes FIC, Japan could continue to collect the $10 NO.