Because the city can be crowded, visiting Paris is often easier and more pleasurable without a car rental (the only exception might be in the summer when Parisians go south to the Riviera.)  If you do rent a car in Paris, be prepared to spend a fair amount of time looking for places to park. That is the downside.  The upside?  Well, cruising Paris in a convertible by moonlight, when all the monuments are backlit is... ooo la la! Unforgettable!
For a smart car rental solution in cities see article: Car rental Fortwo in Paris, that's Smart!

The public transportation system (e.g. subway) is very convenient and used by most Parisians on a daily basis (see article: Paris subway system: Le métro)

If you are planning to travel to the countryside (e.g. Provence, the Riviera, etc.) during the summer months, I recommend renting a larger car with air conditioning. Also, no matter where you are planning to drive, if you've never driven a manual before be sure to specify you need an automatic at the time of reservation.

Usually you will get the best rate by reserving your rental car from abroad.

Your options range from discount rental companies (who simply resell the better known brands) to the better known brands directly (e.g. Hertz, Avis, Alamo, etc.) Discount companies work out most of the time, but you do open yourself to problems in some rare cases.

For my last trip to France, I booked a compact-automatic car, which I was to pick up at the Charles de Gaulle airport upon arrival in Paris.  Normally, I would not rent a car at all, but I did so this time because I was told that the place we were to stay at (near the Eiffel Tower) had a dedicated, underground parking space (I was also told don't rent a Mercedes, it will not fit!) and also because I was planning to visit some family in the suburbs near the "rioting neighborhoods" (November 2005). I opted for an automatic because I hadn't driven a manual in some time, and did not feel confident about navigating the tiny streets of Paris while potentially grinding gears. I used a discount car rental company, reselling SIXT.

After debarking from the plane, I went to the SIXT rental counter as planned, but to my dismay, the compact-automatic we had agreed upon was not there.  Instead, they gave me the only automatic they had on hand; a huge station wagon (see grey car on top picture). I'm sure it would have been a lovely car for traveling in France, but definitely not for a stay in Paris.

Alas, it took me thirty minutes to park that rental car in the subterranean, 1920s parking spot (complete with rotating platform!), and one full hour to get the car back out.  The car was completely useless to us, and had become a liability.  The next day, I brought the car back to SIXT and left it there, without bothering to exchange it for another.  I was not a happy camper, but that is the risk you take when dealing with discount retailers since they are not always 100% up to date with what the main rental companies (e.g. their suppliers) have in stock.

Finally, remember that most car rental companies offer discounted rates for various club members or seniors (e.g. people over 65, AAA, Frequent Flyer members, etc.)