Actually, the Declaration of Independence had very little to do with French philosophes. It was very much a Lockean document.
First, some history. After the English Civil War a writer called Thomas Hobbes wrote Leviathan. He basically argued that living outside of state control was so horrible that we would/should accept a ruler with absolute power because any kind of civil society was better than living outside of one.
A little bit later (1690 something) a writer called John Locke write "Two Treaties on Government", in which he argued that the state of nature was not so brutal and that (wait for it) man had some inalienable rights because of his God-given reason and that, finally, man only formed the civil state to pursue "life, liberty and the pursuit of property". He believed that the state was a man-made thing and required our consent in order to be legitimate.
The Americans would not have liked Rousseau on little bit as he argued that the state and society had is bound by its laws and people must submit to them (he calls this the "General Will"). Once these are in place people must conform to them. On the plus side, everyone is treated equally before the law but they are expected to submit to it. Given that the American founders were in the process of rebelling against their lawful rulers, I suspect that Rousseau was not their philosopher of choice.
Locke, on the other hand, fit the bill nicely: "No taxation without representation" is a Lockean argument (I haven't consented to you so you don't get my property), Their argument about "God-given" rights and reason is pure Locke.