"Men are born free and remain free and equal in rights." Was this use inspired by America's declaration for the one in France?

Indeed, this line is heavily inspired from The
Declaration of Independence. The French Revolution's charter was called The
Declaration of the Rights of Man.  Essentially, it was heavily influenced by Jefferson's
writing.  In fact, Jefferson, himself, served as a type of adviser to the writing of the
French charter.  Jefferson "was the US minister in Paris" and was "consulted" in the
composition of the document.  The leaders of the French Revolution were inspired by the
thinking of the Enlightenment as well as the effectiveness of the American Revolution's
interpretation of The Declaration of Independence. The leaders of
the French Revolution believed Jefferson's writing played a vital role in the success of
the American Revolution.  The hope was that drafting a French version of the document
would have had similar results in France.  It ends up that one of the legacies of the
American Revolution was to inspire revolutions in other part of the world, and one of
them was in France.