Paris is as safe as any big city can be, but you should always remain streetwise and alert. Certain neighborhoods are more seedy than dangerous, thanks to the night trade that goes on around Les Halles and St-Denis and on Boulevard de Clichy in Pigalle. Some off-the-beaten-path neighborhoods (particularly the outlying suburban communities) may warrant extra precaution. When in doubt, stick to the boulevards and well-lighted, populated streets; keep in mind, however, that the Champs-Élysées, Notre Dame, and Louvre areas are a haven for pickpockets.
The métro is quite safe overall, though some lines and stations, in particular Lines 2 and 13, get dodgy late at night. Try not to travel alone late at night, memorize the time of the last métro train to your station, ride in the first car by the conductor, and just use your common sense. If you're worried, spend the money on a taxi. Pickpocketing is the main problem, day or night. Be wary of anyone crowding you unnecessarily, distracting you, or leaning into you. As much as possible, try to blend in and speak softly (as the French do). Pickpockets often work in groups—and they move fast; on the métro they usually strike just before a stop so that they can leap off the train as it pulls into the station. Be especially careful if taking the RER from Charles de Gaulle/Roissy airport into town; disoriented or jet-lagged travelers are vulnerable to sticky fingers.
Pickpockets love bling and won't miss the opportunity to yank off a necklace or follow a tourist wearing a flashy girl's-best-friend on her finger. They often target purses and laptop bags, so keep your valuables on your person. It’s also wise to distribute your cash, credit cards, IDs, and other valuables between a deep front pocket, an inside jacket or vest pocket, and a hidden money pouch. Don't reach for the money pouch once you're in public. If someone holding a map, even a well-dressed woman, asks for directions, go against your helpful American nature and keep walking. Also be wary of the "ring trick" when a passerby suddenly stops in front of you to pick a gold ring off the ground and then offers to sell it to you.
A tremendous number of protest demonstrations are held in Paris—scarcely a week goes by without some kind of march or public gathering. Most are peaceful, but it's best to avoid them. The CRS (French riot police) carefully guard all major demonstrations, directing traffic and preventing violence. They are armed and use tear gas when and if they see fit.
Report any thefts or other problems to the police as soon as possible (note that officiers wear a badge indicating what languages they speak). There are three or four police stations in every arrondissement in Paris and one police station in every train station; go to the one in the area where the event occurred. In the case of pickpocketing or other theft, the police will give you a Déclaration de Perte ou de Vol (receipt for theft or loss). Police reports must be made in person, and the process is helped along by the S.A.V.E. assistance system for foreign victims—a multilingual software program that files your complaint (and provides you with a receipt) in English. You can also pre-file an incident of theft report in French online at www.pre-plainte-en-ligne.gouv.fr; this saves time on the paperwork, although a visit in person to the police station will still be necessary. Valuables are usually unrecoverable, but identity documents have been known to resurface. You may need your receipt of theft or loss to replace stolen train or plane tickets, or passports; the receipts may also be useful for filing insurance claims.
Although women traveling alone sometimes encounter troublesome comments and the like, dragueurs (men who persistently profess their undying love to hapless female passersby) are a dying breed in this increasingly politically correct world. Note that smiling automatically out of politeness is not part of French culture and can be quickly misinterpreted. If you encounter a problem, don't be afraid to show your irritation. Completely ignoring the dragueur should be discouragement enough; if the hassling doesn't let up, don't hesitate to move quickly away.
A few words of advice: leave your jewelry at home, and make sure that smartphones and tablets stay out of sight. Don’t talk to strangers. If someone approaches asking you to take a photo, sign a petition, or provide directions, just keep walking.