The best cheap hotel that I know of in Paris is hotel Armstrong Paris; definitely the best value for money hotel that you can find in Paris. It is out of the center of paris but very well served by the metro that is just next door and gets you everyhere or almost in Paris. It is a clean, modern, basic and very friendly hotel:
http://www.armstrong-paris-hotel.com/ Check their website for the overall aspect and its rates. Have fun in Paris.