“and the French would not have had the authority of law to come to the aid of the US.”
Do you think the French gave a fig if their actions were legal? Or, at least, any more legal than other wars they fought from time to time (which, I’m sure, at some point involved interfering in another nation’s sovereignty)? They were out to hurt Britain, little more.
“the United States would not have been recognized as a Federal Union of Sovereign Political States by the rest of world”
The USSR was eventually internationally recognized even though a lot of people basically still considered them a murderously criminal empire (maybe not FDR, who loved his Uncle Joe, but others). It’s realpolitik.