Paris is not much more dangerous than any other metropolis. The main danger for tourists here are pickpockets - they are active in public transport, the most touristy places (like the queues for the Eiffel Tower) and in shopping centers.
Do not carry large sums of money, wear a shoulder bag, do not shine expensive gadgets. Beware of scammers! They can offer you to buy something from hand, win a large sum in "thimble", "accidentally" get your clothes dirty and offer to clean them — there are a lot of tricks.
And, of course, avoid night visits to Paris District 20, the Bois de Boulogne and other similar places. In case of any emergency, do not be afraid to contact the Commissariat — they will help you (there are special reception points for foreign citizens).
Just in case, read the safety instructions for visitors to Paris before departure.
