Hey Jaryd. I am Nathalie and I can answer to you.
Getting a french bank account is a good idea but not necessary if you stay only 3 to 6 months.
You can propose to the owner of the apartment to pay him for the compete period + the reservation. If so, He will probably agree even if you don't have a job in France.
If you need help to find an apartment, my job is to find apartment for people in Paris. I live in Paris and I am always enjoying working with foreigners.