Probably the fastest method of getting to central Paris is by RER, approx. 30 minutes each way. Since you would want to be at the airport 2 hours before departure, factoring in getting from your arrival point to RER, would give you about 4 hours of free time.
Do you like museums? The Louvre, Orsay and Pompidou are some of the big (and famous) ones.
Is shopping your forte? The "Grand Magasins" in central Paris are great for you.
Dining, Paris is renowned for great restaurants, but many stay open from 12pm-2pm for lunch and then reopen around 7 pm for dinner.
But, walking in various sections can be fascinating, the Paris street scene is really interesting, especially areas like the Latin Quarter, Champs Elysees each different its own way.
Monday and Tuesday are closing days for museums, city and national respectively.