This is pretty common on the RER trains, especially as you roll through the suburbs
If you get on at the right time, you can see multiple bastards in the car, sizing up the passengers and their belongings. One of the common stops is Chatelet-Les Halles train station, which is full of hoodlums waiting to make a little bank off of RER passengers - watch your stuff!
The same rules follow in Paris as they do on other trains and metros - Keep your handbag/daypack strapped on and in front of you, and if it fits, keep your luggage in front of you, between your legs. A good example of this is in Barcelona, where even all the locals hold on to their shit for dear life!