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For a rent of 400 euros, you won’t have any issues with a deposit of 615 euros per month. Check out our article detailing the monthly expenses of a student in France, and how to reduce your expenses. Generally, to reserve accommodation in France, you need to pay the deposit and one month’s rent. So yes, it will be sufficient for the housing aspect.
There is no perfect date to arrive in France as a student. If the question refers to filling out the visa application form, you should plan for one to two weeks before the start date of the courses.
We hope we’ve answered your questions.