So I'm currently in France on a student visa. Can I stay in France under a tourist visa (for 3 months under the Schengen policy) if I decide to stop studying?
Time spent under a long-stay visa (including student visas) does not count toward the 90-day maximum stay in the Schengen area. This rule is defined in article 5 for the Schengen Borders Code (regulation EC 562/2006):
Periods of stay authorised under a residence permit or a long-stay visa shall not be taken into account in the calculation of the duration of stay on the territory of the Member States.
- If you don't need a visa (see the list of “annex II” countries on Wikipedia), you can indeed stay for another 90 days in the Schengen area.
- If you do need a visa for short stays, you could in theory come back to France immediately on a Schengen visa but you would first need to go somewhere else to apply and wait for this visa. Depending on your circumstances, getting this visa might prove difficult.
See also this question on the travel sister site.