The one I knew is sadly gone, and turned into a designer place at five times the price.
At times of year when there aren't many American students around you could try anywhere listed in that year's Lets Go France guide - which usually researches its cheap accommodation options pretty thoroughly.
try this one: http://www.hotel-chopin.com/ otherwise there is a really cheap hotel called Trianon in rue de l'ancienne comedie in the 6th arrondissement. But I know that Hotel Chopin is very good value.
Two we've stayed in that were friendly, clean and good value (many more that we'd warn you against!!):
Hotel des Arts (Montmartre) http://www.arts-hotel-paris.com/
Timhotel Palais Royal (just up from the Louvre)
Timhotel Montmartre (windows looing straight out to Sacre Coeur - if you're on the top floor)
both part of Timhotel chain (http://www.timhotel.com)
The best booking site we've used is Venere (http://www.venera.com) which lets you search by area, price and see reviews from previous guests. World Reservations (http://www.worldres.com) also came up trumps previously. Also http://www.laterooms.co.uk and remember sometimes (usually?) the booking sites get better rates than you can by going direct to the hotel. So call the hotel for a price, but before you confirm do the rounds of the booking sites above to see if you get a better rate.