Cheap travel from Paris

You can use http://kelbillet.com with the cities and date to see different options.

Bus

Bus is slow, cheap (except last minute), comfortable, quiet, can provide light, fresh air, power outlet, wifi, toilets.

http://flixbus.com
http://ouibus.com
http://eurolines.com
http://megabus.com (for UK)

Car-sharing

Car-sharing is quicker than bus and slow train, very flexible for time and places to pick up and drop, cheaper than train and sometimes bus, often the best last-minute choice.
Comfort depends on the car, your seat, the number of people ; you can socialize with people or endure silence or driver-chosen music, no wifi, no power outlet.

http://blablacar.com the most famous and successful, includes a 20% website fee, you may need a phone number to book a ride
http://covoiturage-libre.fr
http://idvroom.com
https://eco-voiturage.fr

Train

TGV is quick (up to 300 km/h) and expensive, you can buy a cheap prem's ticket up to 3 months before. You can even change your mind last minute and resell the ticket.
TER is the slow train, slow and expensive unless you have a discount card.

http://voyages-sncf.com the official website
https://thello.com France-Italy night trains

http://kelbillet.com and http://trocdestrains.com to sell and buy prem's ticket people decided not to use. More demand than offer. Beware of scams.

Plane

Plane is quick (except for the time lost going to the airport, security checking, some margin), noisy, stressful, limiting in what you can carry.

http://ryanair.com (from Beauvais, 17 € bus or 8 € car-sharing, see Cheap Paris)
http://wizzair.com (from Beauvais ; cabin luggage even smaller than usual)
http://easyjet.com in Europe
http://wowair.com proposes cheap flights to USA by Iceland

http://vueling.com mainly Spain and Italy

http://airfrance.fr France main company, don't expect cheap prices

I can't list all whatever, to find flights: http://google.com/flights http://kayak.com http://skyscanner.com