Alexander Hamilton, when asked why the US Constitution made no mention of God or His inspiration, answered "the country did not require foreign aid". When pressed for a more serious answer, he replied, simply, "we forgot".
As far as the French, they weren't motivated by divine intervention (or at least had plenty of natural reasons to act as they did to make their aid something less than proof of a miracle). They hoped America could bloody England up a tad as revenge for the Seven Years War (and a million other affronts over the years of empire collision) from the beginning.
Louis was giving livres, secretly and covertly, before the Declaration even was released. You'd be amazed at how many letters from and between the Committee of Secret Correspondence I've read the past month as original source material related to arms smuggling through the Caribbean and what America would have to show in terms of results to get more French aid and all that.