Paris is a very safe city, and rates of violent crime, especially, will almost certainly be much lower than comparable cities you're used to. Gun crimes are very rare as there is a strictly-enforced ban on personal handguns.
The most common threat to tourists and residents alike is that of having your pocket picked or your bag or mobile phone stolen. Incidents of muggings involving cell phones being grabbed directly and violently out of victims' hands on the metro and on the street have been on the rise for about a year. Police and RATP officials advise to keep smart phones out of sight and safely guarded so as not to attract attention of theives.
As in any large city, keep a close eye on your possessions, never leave your bags unguarded and keep your bags firmly closed - no rummaging to get your metro tickets or fumbling in your pockets at the ATM!
When you are on the metro, you should be especially vigilant if two or more people crowd you. The metro pickpockets work in teams, however they are usually recognizable to the metro driver. If a driver sees a te…