The best explanation of how the American, French, and Haitian Revolutions are related is:
Debt from supporting the American Revolution led King Louis XVI to raise taxes at the Estates-General. The Third Estate objected to new taxes and wrote the Declaration of the Rights of Man and of the Citizen. The declaration inspired a revolt of the enslaved population in Haiti.
This response captures the cause-and-effect relationship between the revolutions, linking financial strain from the American Revolution to the political upheaval in France, which in turn influenced revolutionary movements in Haiti.