People using a bicycle in Paris represent now close to 2% of the global traffic. That means you have something like 40 000 person riding a bicycle every day. This is probably due to the Velib system (http://www.en.velib.paris.fr/) : you can pick a bike in one of the 1200 stations, there are more than 16 000 bicycles available.
How much does it cost ? 1 euro, and you can use the bicycle of half an hour. The ticket is still valid for 24 more hours, but you have to pick a new bicycle every 30 minutes. Considering that most of the trip will take you less than half an hour in Paris, that's enough (Paris is 13km x 7km wide, but don't expect to cross all Paris on those bikes in less than half an hour !)
Last year, those bicycles have been used 26 000 000 times !
I'm using a bicycle in Paris since 1991, and I must say that things have changed a lot since then. I never felt in danger, but I'm used to ride my bike now, even if I'm going fast (probably more than 30 Km/h, when I'm not stopped by a red light).
The rules are simple, if you want to have a safe ride :
I may cumulate something like 2000 kms a year in Paris, day and night, and I must say it's quite a pleasant way to move from one place to another, assuming you have a safe place to store your bicycle.