I (U.S. citizen) studied abroad in France from August 2017 to May 2018, but the visa issued to me -- Type D, multi-entry -- is for the entire year (e.g. August to August).
My understanding, then, is that I can legally stay, even if my study program is over since my visa/residence permit doesn't expire until August 2018.
Is that correct?
Additionally, I have a question re: the 90/180 day rule.
I know that I can travel to other Schengen zone countries for up to 90 days within a 180 day period by using my visa. However, I would like to know if these days count toward the 90/180 day tourist visa rule, or are these 90 days separate?
For example, let's say I travel to Austria while I have my French student visa for 90 days. Then, my French student visa ends, and I leave the Schengen zone. Will I have another 90 days that I can use to stay in the Schengen zone, or would my stay in Austria count towards this time, barring me for 180 days? Also, how does this work practically since there is virtually no border control between Schengen countries? How would they be able to count the days of my stay in other Schengen countries while I'm on my visa?