Paris is generally safe but requires standard urban vigilance. Pickpocketing is the primary concern, concentrated around the Eiffel Tower, Sacré-Cœur, the Louvre, and RER stations (especially RER B to CDG airport). Keep bags zipped and in front. The 'petition scam' near tourist sites involves groups surrounding tourists with clipboards — decline firmly and walk away.
Most Paris neighborhoods are safe to walk at night. Areas around Gare du Nord and Gare de l'Est warrant extra alertness late at night. Violent crime against tourists is rare. Pickpocketing on the Metro is the most consistent risk — hold bags in front on crowded lines (especially 1, 4, and the RER).