In general, Paris is quite safe and street assaults happen rarely..
The city is very well lit, and the metro, the most used method of transport by tourists does not present dangers, not even at night (it runs until past midnight).
Certainly as a tourist who doesn't know the city well, limit your night time wanderings to the more populated areas but by no means be afraid of Paris at night, the city is worth seeing after sunset too! However it's important to have some information for safety in Paris, like emergency numbers, the contact info for your embassy and how to avoid unpleasant experiences.
Saying that, while it is not necessary to walk the streets of Paris in fear, pickpockets are rife in the city so it is important use some common sense when it comes to your personal belongings.
In crowded, touristy areas around the Eiffel Tower for instance or anywhere on the metro during rush hour it pays to be a bit more careful to assure your safety in Paris.
For example, if you keep your wallet in your back pocket it is very likely that at some point it will disappear. Try to carry bags across the front of your body, rather than the back, as it is less tempting.
Most of all just take the usual precautions: carry only the money that you need, your passport, credit card and other important documents should be carried in a pouch that its out of view and not easily reached by pickpockets' hands if you need to keep in on your person at all. Preferably leave them in the hotel's safe or a safe-deposit box.
When it comes to safety in Paris, it is important to know that there are groups of con artists, and children are often part of them. There are a few age-old classics: tragic tales that require money, rolls of bills “found” on the street and distraction methods such as spilling mustard onto your shoulder whilst they grab your bag. This is not to say you should be wary of every small child and pot of mustard, but just be aware pickpockets in city crowds, especially on public transportation and around major monuments.
In a crisis, the most important thing to do is stay calm. If in doubt go to your country's embassy as they will be best placed to help you out.
Most of the following services operate 24 hours a day.
A booming metropolis, Paris has numerous hospitals, and non-French speaking travelers will be pleased to find that often the staff will speak English. While treatment can be expensive, French healthcare is more than adequate.
There is no drinking age in Paris, but to purchase alcohol one must be at least 18 years old. The legal blood-alcohol level for driving in France is .05%, which is less than it is in countries like the US, UK, New Zealand and Ireland so exercise appropriate caution when driving in France.
The French Revolution may have been in 1789, but the spirit of the revolution certainly hasn't died. Protests and strikes are frequent in Paris, and all over France,over anything from the minimum wage to Sarkozy's wardrobe choices, but violence does not often occur.
You may find yourself in the city on the day of a transport strike in which case you may find yourself feeling extremely angry with the French and hating their need to protest. Transport strikes can be some of the most disruptive, but the best thing to do, from experience, is try to work past your rage and just accept the accidentally extended holiday.
The strikes generally don't last more than a week and you could be stuck in worse places!