A good source for flat rentals in English is the FUSAC, an English language want ad paper based in Paris. Their website is here: FUSAC - Petites annonces pour anglophones de Paris

The paper carries both agency ads and individual ads - check the "small ads" section of the website for those that may avoid the agency fee. But the notion of "good sized apartment" in Paris may be disappointing. Paris flats tend to be rather small - and rents are high. Still, see what's on offer in the FUSAC and maybe you'll get lucky.
Cheers,
Bev