Take the RER B blue line to Paris. You can buy the ticket on a vending machine or at the ticket counter. Price is the same, machine is usually faster. I am not quite sure which station you have to get off. Probably either change trains from RER to metro at Chatelet or Les Halles and then get off at St. Germain des Pres, or, if it is closer to Jardin du Luxembourg or St. Michel you can take RER B directly there.
As I said, take RER B directly to Luxembourg, then walk. Should be no more than five minutes in a very nice area, no hills.
You probably walk by a Cafe that's called Rostand on the corner with Boulvd. St. Michel. Have a lait chaud vanille there. Delicious.
http://www.parisby.com/senat/pages/reach.htm
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