Yes, you will need an address to apply for a permit here. As you're an EU national it shouldn't be too much of a problem, you just apply for your student permit once you get an address - hotel, room share, etc.
According to this you have 7 days after your arrival to make your application for a residence permit. http://unige.ch/international/Futuretudiant/etudiantregulier/permis_en.html
Have you contacted the uni's Housing Office for assistance?
I don't think you can study in Switzerland and live in France. That would require you to have a French permit, not a Swiss one and wouldn't allow you to study here.
Don't forget you also need to arrange health insurance cover.