One thing to be aware of is that there are two main legal frameworks for long term rental in France : 'meublé' (furnished) or 'vide' (empty). A 'meublé' will include all furniture (bed, chairs, table, maybe tv set, ...,) whereas a 'vide' rental might include some kitchen stuff (oven, fridge, ...) but no other furniture.
Some clues here on 'meublé' vs 'vide'.
Most important difference : if you rent a 'meublé', the contract is for one year, whereas the contract for a 'vide' apartment is for three years. French law is quite protective for the renter (I mean you, not the owner), especially for 'vide' rentals.
Also, when renting, you have to take into account 'charges' (that might be or not included in the displayed price, look for 'charge comprises' or not. This is what you pay for various stuff mainly related to maintenance of the building/place you're renting.
Then come taxes. You will probably required after one year to pay for 'taxe d'habitation'. That is what the city you are living in will ask for taking charge of city's duties (garbage, streets, ...). It is based on a complex and outdated algorithm mostly related to the surface of the the flat/house, but it's ratio varies from town to town.
Once this established, looking for a rent in the Paris area is a difficult (unless you have excellent credentials and a large amount of money) task. Even for native french. The way thing goes :
- you find an interesting announce
- you contact the owner (or it's
representative) to actually visit the place
- they ask for a bunch of documents (mostly based on the idea you are a french national, that include payslips, tax documents, proof that someone will pay for your rent in case you cannot, ...)
- after a while, they say 'yes' or 'no'
Now, to the question :
https://www.leboncoin.fr/locations/offres/ile_de_france/ is a starting point.
http://www.pap.fr/annonce/location-appartement-maison-ile-de-france-g471 is another option