Hi, and welcome to the forum.

Living near Paris, I no longer have to worry about where to stay in the city - but there is a book out called "Cheap Sleeps in Paris" that used to be my bible on where to stay in the city. Their write-up of the hotels was very good - they noted what places were "typically Parisien" and which were just kind of groady.

That said, there is a very cheap hotel that I see from the RER when I go into Paris. It's just outside the city, near the "Cité Université" and the sign outside promises rooms for 49 euros a night. I don't think I'd want to stay there, though.

My favorite hotel from Cheap Sleeps is certainly the Hotel Istria in the 15th - Hotel Istria - OFFICIAL SITE - Paris Montparnasse Istria Hotel - but I suspect the rates have gone up considerably since I last stayed there. The family that owns the place is really nice - and it pays to book in advance (or according to the website, at the last minute if there are vacancies).
Cheers,
Bev