My bag got snatched on the train in from CDG to Gard du Nord fortunately, the guy was a bit of a novice, so i managed to get everything back except the cash by shouting at him (he didn't run off, he stood and went through it behind me and i caught him - since he didn't know how the rest of the train would react, he backed down). So it could have been a lot worse.

Having got off to a bad start, Paris managed to entrance me completely. Didn't have any more problems after that, although I did go into super paranoid mode. Travelled the metro at night without problems, although I did take normal precautions. So be aware of yourself and your surroundings... you should be fine.