If university accommodation is not an option, I think that Fusac magazine (mentioned by Christina) might be the best place to look for ads. It's aimed at Americans in Paris (the acronym in the title stands for France-USA-Contacts) and it's always full of ads for short, medium and long-term rentals, and furnished accommodation (which is hard to find in Paris outside the holiday rental market). The only problem is that the website lists just a tiny fraction of the ads printed in the magazine, which is distributed free of charge in many bars, English bookshops (e.g. WH Smith on rue du Rivoli or Brentanos on Ave de l'Opéra), etc. around Paris.
Standard estate agencies are unlikely to be helpful in your situation as few rent out furnished apartments and they aren't usually keen on short rentals.

I'd also suggest keeping your options open by widening the area that you are searching in (e.g. 13th, 14th arrondissements).

I would go through the official student rental sites, because they handle all of the details like the rent guarantee, obligatory insurance, etc. (why pay insurance for 1 year when you only have an apartment for 9 months?)