American war of independence and 2nd Mysore war
Everybody knows the AWI, but the 2nd Mysore war is lesser known. But here you have the French fighting the British too. So you could see it as part of the AWI.
Take a look at Wikipedia - https://en.wikipedia.org/wiki/Second_Anglo-Mysore_War
Take a look at Wikipedia - https://en.wikipedia.org/wiki/Second_Anglo-Mysore_War