I am traveling to Paris for a month's time. I would like to visit nearby countries like Luxembourg, Spain, Switzerland etc.
Can you please suggest some cheap travel means?
If you want to have a favourbale price for train travel, you have to book early and to be flexible. The Man in Seat 61 is providing more information on train travel. Although his trips start in London, nearly all of them transit through Paris.
Flying can be interesting too, especially for longer trips such as e.g. Spain. You have some low cost carries operating from Paris or nearby (Easyjet, Vueling, Ryanair, ...). Note that Ryanair is operating from Beauvais, 80 kilometers outside of Paris. But other conventional carries can have competitive prices too. Just check specialized sites, such as Kayak or Matrix Airfare Search.
Take the plane with a low cost company like easy jet or ryanair. The West europe part is easy to access and pretty cheap.
You can use website like enter lastminute.com