I'm not sure there is any easily available 'zones' map, but the basic principle is to have the kid go to the closest school (and somehow, someone somewhere must have a map...)

Here's already the schools list for a start: https://www.ge.ch/primaire/communes/geneve-ville.asp

I hope this helps.

I have also gone looking for such a map in the past and have not been able to find one. I doubt one exists to be honest. As David says, its going to be the closest school to your home but it can be strange, for instsnce you might have kids going to a different school to kids living across the street from you. If there is a school you would particularly like but its not your closest, you can write requesting a change, you might have to give a convincing reason. Seems quite a common thing to do.