No vista is required if you stay for under 3 months. It is usually better to wait for special roundtrip tickets to paris for $300 - $600 than buy a one way ticket for $2000. Just 'accidentally' miss your flight back if you want to stay. Even if you do not want to go to Paris, public transportation is cheap there and you can go by bus to any city.
You must go back to your home country to renew a student visa or get one, without exception. Many colleges like foreign students to have the TCF.
The French consolate will require you to show you have at least 1000 euros per person per month in order to grant a Visa. Visitors can work in France, the minimum wage is around $11 and hour (or $9 after tax).
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