Both the Bill of Rights and the Declaration provided protections to ensure that anyone accused of a crime had the right to a fair trial. Thomas Jefferson played some role in influencing the drafting of both. And certainly the ideas of major Enlightenment philosophers, such as Montesquieu and Rousseau, provided the intellectual framework for assumptions about individualism, freedom
But the similarities end there. While France and other European countries have updated their constitutions to include economic, social and cultural rights (with some including environmental rights as well), the US has not ventured beyond civil, political and property rights, and the Bill of Rights has only been gingerly expanded, chiefly to abolish slavery and expand voting rights for Black people and women.