Question

which action by the National assembly was inspired by enlightenment ideals and the American revolution

Answer 1

It was primarily the action of eliminating the monarchy that was inspired by enlightenment ideals and the American revolution, since the French Revolution was ultimately about creating a democracy and removing the King and Queen from power. 

Answer 2

The correct answer is: "the derrocation of the absolute monarchy and the defense of popular sovereignty".

The age of Enlightment, was the age of scientific thinking and reason and it broke with centuries of religious dogmatism and with the many institutions of the Ancient regime that laid on those foundations, such as the absolute monarchies. These ruled most Western European countries, and many were derrocated by the revolutions that ocurred in many countries such as in France (the French Revolution).

The National Assembly was a chamber founded by the representatives of the Third Estate, who denounced the lack of representation they enjoyed on the kings's assembly, known as the Estates General. This old assembly did not pay attention to the needs of the Third Estate and hence, it did not listen to the majority of the unprivileged population that formed the Third Estate and these were the ones who founded the National Assembly, revolted against the king and his absolute power and who enacted a new Constitution that included new rights for French citizens. They claimed for popular sovereignty and for the right of citizens to elect their representatives through suffrage.

The ideas of the French Revolution, specially the popular sovereignty claims, inspired the subsequent American revolution. Americans did not want to be ruled by foreign kings that they have not chosen.