How did the declaration or independence influence the writing of the declaration of the rights of man and the citizen?

The Declaration of the Rights of Man and the Citizen was  written in consultation with Thomas Jefferson of the United States, who had drafted the Declaration of Independence.

Abbé Sieyès was a prominent clergyman in France who supported the rights of the common people.  The Marquis de Lafayette was a member of the nobility who had fought in America's war for independence against Britain.   In writing their declaration for France, they drew inspiration from America's founding document and indeed consulted with Thomas Jefferson.

The Declaration of Independence (1776), written by Jefferson, asserted the American colonies' decision to break away from British government.  It included the same Enlightenment ideals of natural rights and liberties that would characterize the Declaration of the Rights of Man and Citizen produced later (1789) in France.

The Declaration of the Rights of Man and Citizen was approved by the National Assembly of France on August 26, 1789, in the early months of the French Revolution.