Airport is closed from 0:00 to 4:00 -- from the website FAQ section:
".For security reasons, the airport is closed from 00:00 to 04:00. Unfortunately passengers are not allowed to stay inside the terminal while the airport is closed. More than 130 hotels in all price ranges in Geneva: the choice is yours.
Consult the full list of Geneva hotels, safely book online. If you cannot afford to go to a hotel, we recommend that you contact a Geneva youth hostel, +4122 732 62 60 or +4122 901 15 00".