As we have seen in the answer to your question in the link below, there are three main Enlightenment ideas that influenced the American Revolution and the French Revolution. The first of these is the idea of popular sovereignty. This idea holds that the people should have the ultimate power over the government. The second idea is that of individual freedoms. The government should protect the rights that people have by virtue of being human. Finally, there is the idea of political and legal equality. The law should treat every person equally, regardless of whether they are rich or poor. These ideas informed Thomas Jefferson as he wrote the Declaration of Independence and they (and Jefferson) influenced the Declaration of the Rights of Man and the Citizen.
Article 1 of the French Declaration says that all men “are born and remain free and equal.” This clearly echoes Jefferson’s phrase from the Declaration of Independence. Both declarations take this idea from the Enlightenment idea of political and legal equality. Article 2 of the French Declaration says that the goal of all governments is “the preservation of the natural and inalienable rights of man.” Jefferson’s Declaration of Independence says that governments are formed “to secure these rights” (“these rights” are “life, liberty, and the pursuit of happiness”). Again, both formulations come from the Enlightenment idea that people have individual rights and freedoms. Finally, Article 3 of the Declaration of the Rights of Man and the Citizen says that “all sovereignty resides essentially in the nation.” By “nation,” it means “the people.”
In looking at these passages from the Declaration of the Rights of Man and the Citizen, we can see very close connections to the American Declaration of Independence and to the ideas of the Enlightenment.