I've been toying with an idea that puts King Louis XVI, Marie Antoinette, and the House of Bourbon on the throne of a monarchist United States. The POD is that George Washington, in 1781, decides to invade New York City (his favored tactic) rather than go with Rochambeau's plan to stop the British at Yorktown, Virginia. The invasion of New York goes horribly, the Americans are repulsed, and the Brits gain a foothold in Virginia. The American Revolution then continues on for a few more brutal years, and it only ends after numerous French victories over the Redcoats.
This extra spending in the Revolution speeds up the downfall of the House of Bourbon and the rise of the French Revolution. As the United States is deliberating at its Constitutional Convention (where, due to the prolonged years of conflict, a strong federal government or a constitutional monarchy are the two most favored proposals), Lafayette and the French Royal Family flee Versailles and set sail for Philadelphia. Eventually, the United States becomes the United Kingdoms of America, with Louis XVI as King of the American People, and George Washington as the first Prime Minister, or President, or Governor, or whatever.