Paris Accomodations

You might try looking on venere.com or booking.com.
For Paris 100 E is not going to get you much. In all liklyhood, VERY small room, No AC, possibly no fans, and not in an easily accessable area.

Check TripAdvisor as well. Check the B&B's as well

Look at EuroCheapo: http://www.eurocheapo.com/paris/features/where-to-stay-in-paris.html. Be aware that the places listed here are not secrets, so book soon!

Chelsea,
You may want to check Homeaway.com. some of the listings allow daily rates if the Owner cannot book a week. Since they are condos, they usually have AC. You might get lucky. You also get to correspond directly with the Owner and perhaps they will be sympathetic to the nice grand daughter!

Chelsea don't know if you can get rooms at this late date, but I have stayed at both of these hotels. They are clean, they have a/c( good idea for July) they are central central central, but both on quieter streets. Rooms are small, but fine. Hotel Diana Hotel Saint Pierre ( the one near the Sorbonne, several hotels with similar names). Both put you within walking distance to many sites, are 5 minute walk from RER station that brings you in from airport( if you choose to use RER). Both are near many bus lines and metro stations( bus is better choice if granny is not good with stairs). Both have had doubles under 100 euros per night, but at this point perhaps good deals are gone. As I said neither are fancy, but they are clean , cheap and central ( and both have elevators , some hotels don't so don't assume they do unless they say so , especially budget hotels)

I stayed at the Solar Hotel (http://www.solarhotel.fr/en/) a couple of weeks ago and was pretty impressed - they do 69 euro per night including breakfast. It's in a pleasant area of Paris that doesn't have a high tourist profile but does have good transport links. The only thing is that if your grandmother has mobility difficulties you need to make sure that they give you a room in the main building - they have a second building around the corner that is perfectly acceptable room-wise but has no elevator.

Thanks for the helpful advice! Have had success using venere.com and look forward to staying at the Hotel Chopin. I had to compromise in price and go over my budget of 100 euro but the hotel I'm staying in is central, air conditioned and offers a good breakfast.

Try airbnb.com - they are listings by private individuals who let rooms and apartments through this website. We have had great luck with every booking we've made through this site and I have many friends who also use it. We have stayed with people in their homes and also rented apartments. Great experiences! Give it a try...it will certainly be cheaper than a hotel. 100 euros isn't going to get you much in Paris but you should be able to get by on that budget with airbnb.
Good luck!