Apartments in Paris are basically among the most expensive ones in the whole country (along with those in Saint Tropez). I do remember that a proper one (1 bedroom, a kitchen and a living room (not to mention a bathroom ofc)) costs, at least if you wanna remain near the Parc , around 800Ç per month.
Good luck anyway.
Because I noticed your location but I never saw you in the French forum, just wondering. Paris is a nice city if you do know where to go (and better which places to avoid), hope you'll enjoy your journey.