Paris, a city made for walking, has an excellent network of metro lines, buses and RER (suburban rail), the same ticket used by all. Hold on to your ticket until you exit the stations. The Metro and RER close down between 12:30 a.m. (1:30 a.m. weekends) and 5:30 a.m., which means looking for a night bus or hanging out at the boîte until dawn. The city center and airports are connected by public bus, coach and rail. For savings and convenience, look into the Paris Visite travel card for 1,2, 3 or 5 consecutive days in central Paris and close-in suburbs and includes Charles de Gaulle, Orly and Versaille by bus, metro, tramway and RER networks. There is also a weekly smart-card pas.
You don't need a car - or the traffic snarls and parking challenges - while visiting Paris. The public transportation system will get you where you want to go. If you plan to get out and about in France, rent a car at the end of your Paris visit and pick it up on the outskirts of town in the direction you're going - like Orly airport for south or west and Charles de Galle for for points north. Another option is to take a high-speed train to the region you want to explore and pick up a rental car there.
Thanks to Bertrand Delanoë, the first gay mayor of Paris (2001-2014), you can pedal your way around the city on Vélib, a self-service, 24-hour bike rental system on a 1-day or 7-day ticket. Vélib, BTW, stands for "vélo' (bike) and "liberté." The first 30 minutes of every ride is free, and you can buy tickets online. Stations are strategically placed all over the city.
Metro lines, which used to be designated by where they ended, now go mostly by number, so it's useful to consult maps in metro stations or download free apps like the Paris Metro RATP Map. Individual tickets at €1.80 are sold at machines in stations, some tabacs and windows at RER/Metro hubs. You can also buy 10 at once - a carnet - for €14.40. Buying a pass for a limited number of days not only saves you money but gives you freedom to bounce around town..
Buses are a great, cheap way to see the city. Some of the more picturesque routes: #69 from Père Lachaise Cemetery to Eiffel Tower, #80 from Sacré Coeur to Eiffel Tower, #73 from Hotel de Ville to Eiffel Tower. Nociliens, night buses, fill the rail void between midnight and dawn on 47 routes with buses every 15 - 60 minutes depending on route. The same tickets work for bus and metro.
Taxis can be hired at taxi stands or hailed. You'll know the taxi is free if the roof sign is green. Choose the Metro over taxi during rush hour if you have to get anywhere fast. Be prepared to pay cash. A taxi from Gare du Nord to the Marais might cost you around $12 plus tip. As of now, the French government has barred Uber after taxi strikes.