The stuff of great motion pictures!
An interesting post-battle legal fight came about when John Paul Jones sailed the captured Serapis into the neutral port of Texel (Netherlands) without a 'National Ensign' as the one on the "Bonhomme Richard" had been blown away in the battle. The British representatives wanted to claim that this lack made the action a case of piracy, subjecting the winners to imprisonment and possible execution. Benjamin Franklin and John Adams quickly got a non-standard replacement ensign to the ship that then allowed the Dutch to avoid that legalism!
This is now known as the "Serapis" or "John Paul Jones" flag.