Driving in Paris is not fun.
Paris—like most cities around the world—has crazy traffic, arcane driving rules, narrow streets, and a mind-bogglingly large percentage of one-way or pedestrian-only roads.
Also, you'll probably end up having to go through L'Étoile (the traffic circle around the Arc de Triomphe), which is the ninth circle of driving hell in Europe. (Place de la Bastille at rush hour is a close second. So is place de la Concorde).
If you're coming into Paris by car, you'll end upon the péripherique, the ring road surrounding Paris proper. This thick band of traffic allows you to zip around (well, "zipping" is not always the case at rush hour) to enter the city from the direction closest to the side of town you want to be on.
Frankly, though, if you're headed into the very center it doesn't really matter which exit you take (though you might want to be sure you're headed into downtown on the correct side of the Seine, the Left Bank or Right Bank depending). Just follow signs for "centre ville" (the center of town)—or just the icon of a black-on-white bullseye—and you'll be fine.
Then, as soon as you check into your hotel, get rid of your car.
A car is simply an expensive hassle that will do you no good anyway. There's rarely any legal on-street in central Paris (and what there is is largely for residents only). A sign with blue circle outlined in red with a red slash means no parking on the side of the street where the sign is posted. (If the're a red X, it means no parking on either side of the street, as in the photograph in the left sidebar.)
Here's the solution:
AAA (www.aaa.com) - One stop shopping for International Drivers Permits, traveler's checks, and some free maps and stuff (not great outside of the U.S., but decent for an overview of other countries).
Fuel costs in Europe (www.theaa.com) - The British version of AAA provides a monthly chart, downloadable in pdf format, showing you how much gas (er, "petrol") costs per liter (er, "litre") in countries across Europe. That should be a direct link above, but if not: it's usually kept under "Motoring: Motoring Costs."
The prices might look at a glance to be great—but remember to multiply the per-liter price by 3.8 to get the per-gallon price (then multiply that by the current exchange rate to understand the true cost in dollars). This will give you a sense of just how insanely expansive gas is in Europe. For example, in spring 2012 gasoline ran €1.61 per liter in France.
Do the math, and that's $8.07 a gallon.
Now maybe you understand why Europeans think we're crazy to complain about the price of gas in the U.S. (and why they drive such tiny, fuel efficient cars).
Much of central Paris is a "Zone Touristique" with no on-street parking (that blue circle with a red X over it mean no parking on either side of the street; were it just a single red slash, it would mean no parking on the side of the street where the sign is posted).