There are a two or 3 different ways. None of them are easy:
1. If you have a boyfriend living there, he may be able to sponsor you. He will have to prove that he can take care of you and provide health insurance for you.
2. Get a job with a company in France. However, they have to hire you from the US. You cannot go about getting a job while you are there.
3. You can apply for a long term visa from the French Consulate in your area. I believe it is good for up to a year. You will have to prove that you have the funds to live on for a year, as you will not be allowed to work. You must prove that you have health insurance that it is valid in France.
I believe the French Consulate/Embassy has a website where you can download the papers you will need to fill out (in triplicate). It will also tell you what papers you need to provide, how many copies of each you will need, and which papers you will have to have translated into French. I think, but I am not sure, you might have to show that you have a place to live.
After a year, you can get your visa renewed in France as long as you have the financial means to live there and health insurance.
Hope this helps.