The correct answer is: "Both revolutions were influenced by the Enlightenment principles and therefore, Americans sided with the French in their uprising".
The Enlighment movement emerged in Europe in the 18th century and it was constituted by philosophers that promoted Reason and the scientific method over medieval superstition and religious dogmas, and the establishment of democratic societies where the power resided on its people, and not in absolute monarchs or rulers "appointed by God". The resulting states that emerged based on the principles of this movement, enacted bills of civil rights for the first time in history, and implemented principles such as the division of powers or the social contract, through which citizens elected their governors by suffrage.
Such Enlightment principles were transferred to the American colonies, where the population claimed for political representation rather than being governed by foreigners that were appointed by a foreign king. Such claims were ignored and the colonies, influenced by the new democratic principles, started several revolutionary movements for independence aiming to establish new independent states based on the Enlightment principles like in Europe.
The success of the American Revolution served as an example that the French followed intending to liberate themselves from their absolute monarchy and aiming to fight for the establishment of democratic principles in their society too. Therefore, the underlying ideology during the French revolution was the same that during the American uprising and, hence, Americans identified themselves with the French and supported their fight.
