I am not expert in the US, and it has actually nothing to do with my comment, but I believe that police in the US might ask you to identify yourself in some circumstances (which is quite different from having to show an ID).

What I mentioned regarding France is that you must show an ID (passport, ID card or driving license) or face being detained at the police station when asked by police. You do not need to be a suspect of anything to be required to show an ID.