You want to take several Paris day trips over the course of your vacation and cannot or prefer not to rely on the rail system. Do keep in mind, however, that trains can easily take you to popular Paris day trip destinations like Disneyland Paris, the Chateau de Versailles and Fontainebleau.
You or one of your traveling companions has extremely limited mobility. The Paris metro is not particularly kind to users who have trouble walking for long stretches and climbing stairs. Some stations are well equipped for travelers with limited mobility and disabilities, but these are few and far between. However, one alternative may be to take buses-- either the Paris city bus system or hop-on, hop-off bus tours of Paris. If none of these options meet your needs, then consider renting a car in Paris.
Your hotel or accommodations are in a remote area outside Paris and not in close reach of public transport. Even in the outer suburbs, public transport in the Paris region is generally excellent and reliable. However, you may have found lodging in a more remote area where you can't easily commute into the city. In this case, a rental car may be practical-- but I advise parking it at the train station closest to your hotel and using public transport to get to and travel around central Paris. I can't stress enough what a headache it can be to find parking in the city center-- and even those very comfortable with driving abroad may find road conditions stressful.
Still Want to Rent a Car in Paris?Companies including Hertz (book direct) and Avis rent cars from several pickup points in and around Paris and the city's main airports, Roissy Charles de Gaulle and Orly.
In addition, since October 2011, a self-service car rental scheme, Autolib', allows you to rent an electric car for short trips around the city. A subscription is required, however, so it's really only a viable option if you're on a longer sojourn in Paris (two weeks or longer).