The Transilien (SNCF) trains leave from the main transport centers to outlying towns. You can travel fast by SNCF to many destinations around Paris. You can reach Versailles in 20 minutes from the Gare Montparnasse. Fontainebleau is 40 minutes away from the Gare de Lyon.
You can also get around by bicycle in Paris. Velib operates as a self-service system, disposing of many stations in the city. Take a bike at one station and leave it at another, once you complete your ride. This way, you avoid traffic jams and circulate through Paris at your own convenience. Have in mind, though, that you may have issues finding a parking spot in the center.