Do you think I could earn enough money to live if I workas a private tutor ?

I'm french and I wil soon come to America as an au pair for 9 month. But if I don't feel ok with my family, I would like to stay in America and try to earn money in another way.
In France, I am a private tutor, that's my job, and that make me earn enough money to live.

How much money does a tutor earn in one hour of tutoring ?

How much can a tutor earn? To be honest with you, it really depends on a couple of factors. For example, what credentials you have. Also, it depends on the area you will be tutoring in. If it's in a bigger city then you can offer higher rates since there will be more people who need your services (the old supply and demand theory!). If you'd be tutoring in a more affluent neighborhood, you could also charge more.

You must realise that as a private tutor, you can charge a substantial rate but you are restricted to a specific area - smaller market of potential students. If you tutor online, the rate is lower but you can have more students. Think outside the box! Try online tutoring. Then you can have a worldwide market of potential students. Try sites like:

(1) http://www.tuitionplaza.com/tutoring/
(2) http://www.tutor.com
(3) ... many other sites (use search engine)

Yes you could, if you can get enough people to tutor.

I don't see it supporting you in america...the price of living is completely different over here.

most of the tutors work with larger agencies.

some are private. with the right resume you might get clients from a good private school and make really good money. You might still need a second job . check the work Visa.