I would also recommend to always have some ID with you, because of the rather tense context due to the recent terrorist attacks. As stated on this site (unfortunately not translated in english) service-public.fr/particuliers/vosdroits/F1036 , if you can not show a valid ID during a routine check, you may have to go to a police station for up to 4 hours.

Way too short to be an answer, but as a local, I'd say the main difference is that a tourist will answer to the person bothering him/her. Just shake you head as a "No", eventually put your hand in front of you as to keep the distance and that's it, not even a word. Some headphones might also help to notify that you don't want to be bothered, like a real parisian.