As kevlegs said, a lot is covered in the Driving/Transport section, but just to underscore the parking situation - parking in Basel city is ridiculously difficult. Do not bring your car over with the expectation of parking it in the city, but rather with the expectation of using it to get out and about to outlying areas (to sightsee etc) or for the Ikea runs.

If you are working for one of the major companies in Basel in one of their outer plants/campuses, you may find your car more useful to get out there, or if you are living in France (or Germany)/working in Basel, but in that case, make sure your company is going to provide you with parking. Some places have so little parking, they have a lotto for parking spaces, so for a year you might find you can't even drive to work cos there is nowhere to park.

There are quite a few roads and routes in Basel that cars aren't allowed to take, but are tramways only. Please check out your parking before hand, don't rely on finding public parking! It will make things so much easier for you.