There is a group of men who steal people's shit on the trains in Paris to an from the airport. Last winter I had my purse on me and a tote bag next to me. The moment I let go of it, a dude jumped from behind grabbed it and ran off at the speed of light. Fortunately all he got were my level 1 french textbooks, a bunch of make up, toiletries and listerine. The police say they have been a reocurring problem. Just yesterday a friend phoned me and said the same thing happened, except they got her wallet and passport.
So, if you're flying into Paris or taking the train to the burbs, hold on to your stuff.