You've done a good job of listing the number of motivations and interest in the American cause by France. But each of them belong to different people or factions. The king, his army, the people of France, the average aristocrat, Lafayette himself all had different motives, etc.
Sorry madam for correcting you, but this is not a giant boat on her hat --- this is a giant ship. You later on called it a frigate -- therefore, a man'o'war -- not s fisherman's boat.
Academia? A proper and diligent presentation of this subject might require a few hours, while this is an oversimplified, cynical and exaggerated spectacle of a fascinating character who deserves better.