My nephew in France writes:
As a resident alien, I have read about the issue in Arizona with interest. This is what you have to do if you want to stay in France past the limit allowed for passport holding tourists:
1. Purchase the appropriate visa from a French Consulate before you arrive. To attain the student/work visa you have to provide proof of financial means for the time period you are applying for and proof of medical insurance which is accepted in France. They check. If you are planning to work you have to provide proof of employment beforehand; if you are going to attend school you have to have the acceptance letter. They check.
2. Once you arrive, you have X days (I forget how many but it was reasonable) to present yourself to the local police department. There you to have a picture taken, fingerprints made, papers screened, and then scheduled to return for a physical screening by a doctor (with blood drawn, as req’d) after which you are given your carte de sejour.
3. I am required by French Law to carry my carte de sejour at all times and I may be asked to present my ID card at any time, for any reason, to the authorities in order to prove my resident status.
All the above was a pain and each step cost a 100 euro, but if you want to study and/or work in France, guess what, you get a carte de sejour