Depending on what you like to do, you could easily spend all 12 days just exploring Paris, the museums and tourist sites. Then there are the sites just outside Paris - like Versailles. Depending on when you are there, you may get to check out Paris Plage, the Paris beach set up along the Seine during the summer.

But for cheap lodging, you may have to hurry. July is peak tourist season in Paris and reservations go quickly. Find a book called "Cheap Sleeps in Paris" - their write-ups of the various hotels are generally very good, so you can tell what you will be getting for your low tarif.
Cheers,
Bev