It is generally a bad idea to rent a car to visit Paris. Traffic is very dense during the day, and parking tends to be difficult. This is especially true in areas surrounding points of touristic interest, since many of these are in areas designed long before automobiles existed. A majority of Parisian households do not own cars.
Driving may be an option for going to some sights in the suburbs such as Vaux-le-Vicomte castle or the castle and city at Fontainebleau, or for starting to other places in France. You may prefer to rent from a location not situated in Paris proper.
Traffic rules in Paris are basically the same as elsewhere in France, with the exception of having to yield to incoming traffic on roundabouts. However, driving in dense traffic in Paris and suburbs during commute times, can be especially strenuous. Be prepared for traffic jams, cars changing lanes at short notice, and so on. Another issue is pedestrians, who tend to fearlessly jaywalk more in Paris than in other French cities. Be prepared for pedestrians crossing the street on red, and expect similar adventurous behavior from cyclists. Remember that even if a pedestrian or cyclist crossed on red, if you hit him, you (in fact, your insurance) will have to bear civil responsibility for the damages, and possibly prosecution for failing to control your vehicle.
Paris has several beltway systems. There is a series of boulevards named after Napoleonic-era generals (Boulevard Masséna), and collectively referred to as boulevard des maréchaux. These are normal wide avenues, with traffic lights. Somewhat outside of this boulevard is the boulevard périphérique, a freeway-style beltway. The périphérique intérieur is the inner lanes (going clockwise), the périphérique extérieur the outer lanes (going counter-clockwise). Note that despite the looks, the périphérique is not an autoroute: the speed limit is 80 and, very unusually, incoming traffic has the right of way, at least theoretically (presumably because, otherwise, nobody would be able to enter during rush hour).
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Based on a work at Wikitravel.org & Traveldudes.org.