For once I agree with Spidergoat. The Constitution does NOT say that. The Declaration of Independence says that. However your basic point is still valid. Atheists do not believe in rights because rights come from God and noone else.According to the US constitution, I'm not familiar with any European ones
OK, why?
Because it says "all men are Created equal and endowed by their Creator with certain inalienable rights
If you don't believe in a creator, the rest becomes irrelevant.