Is this to actually get the Shengen Visa? That isn't fair if so - you could just be visiting Calais for the day or staying with a friend. If so, book one of the posh hotels which has a no cancellation fee policy... and then cancel once you get the Visa. We were never asked for a hotel reservation.

Paris doesn't do cheap hotels unless you're lucky (Terpe's suggestion is worth a look for sure). One of my favourites is Le Tourville:

http://www.paris-hotel-tourville.com/fr

Of course there are thousands around the same price.

Another option is to look at offers from Easyjet or whichever airline you're travelling with (or Eurostar's website).