To understand America's founders, we have to realize what Dr. Michael Novak of American Enterprise Institute has said. He observed that thinkers we call men of the "Enlightenment" are really of two sorts. There are those who believed in God and those who didn't.
The French Revolution was history's first secular revolution---and, incidentally, spilled rivers of blood. They chose to follow the unbelieving thinkers of the "Enlightenment" ---e.g., Voltaire, Diderot, Rousseau, and David Hume. But our founders quoted those men of the "Enlightenment" who believed in the Lord---e.g., Montesquieu, John Locke, and Sir William Blackstone.
In his The Spirit of Laws, Baron Montesquieu wrote: "We shall see that we owe to Christianity, in government, a certain political law, and in war a certain law of nations—benefits which human nature can never sufficiently acknowledge."
I used to have a Sunday school teacher who became born again while earning his Ph.D. at Yale. He studied John Locke in depth. Locke not only wrote his Second Treatise of Civil Government, which was influential to our nation's founders; but he also wrote The Reasonableness of Christianity. As my teacher read Locke in his own words, he came to embrace Christ.
Sir William Blackstone, the great British jurist, was important to our founders and is still quoted by the Supreme Court sometimes. Blackstone wrote of "the law of nature and the law of revelation"---like "the laws of Nature and of Nature's God" in our Declaration of Independence.