Renting a bike is a very good alternative over driving or using public transport. Riding a bike anywhere in the city is far safer for the moderately experienced cyclists than almost any town or city in the United States. The French are very cognizant of cyclists, almost to a point of reverence. A few years ago Paris wasn't the easiest place to get around by bike. That however has changed dramatically in recent years, starting perhaps with a lengthy bus and traffic jam. The city government has taken a number of steps in strong support of improving the safety and efficiency of the urban cyclist as well, in establishing some separated bike lanes, but even more important a policy of allowing cyclists to share the ample bus lanes on most major boulevards. Paris also has many riversides which are perfect for cycling as well. The Paris bike network now counts over 150 km (93 miles) of either unique or shared lanes for the cyclist.
You can find an excellent map of the bike network called Plan des itinéraires cyclables (download here) at the information center in the 'Hôtel de Ville.
* In July 2007 the municipality of Paris introduced the Velib program ("vélo liberté", Bicycle Freedom, see the french site  or an english description , where it is possible to rent a bike for a very modest price. Numerous stations are to be found around the city; with your credit card, you can subscribe for 1 day (1€) or 7 days (5€) & then get a bike; the first 30 mn are free... so the game is to get to another station in 25 mn & get another bicycle (you will have to wait for 5 mn before you get another one, though)...Try it, it's great!
Bikes can also be rented from numerous private vendors, including Fat Tire Bike Tours, Bike About Tours, and Roue Libre, a joint project of the Mayor's office and the RATP.
To contact Fat Tire Bike Tours  call their office at +33 6 56 58 10 54,. They are open daily, and rentals are €2/hour, €15/day, €25/2 day period, or €45/week. They are located at 24, rue Edgar Faure, 75015. Fat Tire also provides daily tours.
The Bike About ( 06 21 18 46 93)  rental point is located in the center of Paris at the Vinci Car Park, just behind the town hall or "Hotel de Ville" (Rue Lobau). They are open daily, and rentals are €15/day, €25/2 day period. They also provide guided bike tours of Paris, given by local, English-speaking guides who know the city well. This is a great way to experience Paris. They are one of the smaller tour companies in Paris & give you a great insiders look at the city.
In addition to operating a number of bike rental buses, the RATP has some permanent locations, including:
* Roue Libre Les Halles, . 1 passage Mondétour (face au 120 rue Rambuteau), Métro: Les Halles. : +33 8 10 44 15 34. Opening hours from 9 a.m. until 7 p.m. Bikes can be rented for one weekend (€25), Monday to Friday (€20), a working day (€9), or one day in the weekend (€14). * Roue Libre Bastille, . 37, boulevard Bourdon, Métro: Bastille. +33 1 44 54 19 29. Opening hours from 9 a.m. until 7 p.m. Bikes can be rented for one weekend (€25), Monday to Friday (€20), a working day (€9), or one day in the weekend (€14).