Very interesting battle. It seems the French forces had some spy information that helped them know what units and defenses the British had on the island. And the British guards had been out drinking the night when some French forces landed (allowing them undefended access early on).
However, the British far outnumbered the French forces and called their bluff to surrender the island. After some short fighting, many of the French were captured. The island served as a British control point on an American-French supply route. I wasn’t very familiar with this battle before this, thanks for mentioning it.
I have added up an image of the Copley painting, it really shows the action.