I should add that it is your Swiss employer who needs to apply to the Canton on your behalf, preferably before you actually start work.
Note that it is the canton (not the commune) that deals with 'G' permits.
This user would like to thank lux_interior for this useful post:
Does anyone know the correct procedure/sequence if one is already working and residing in GE (B Permis held) and moves to France?
I presume the company must still apply for the 'Frontallier' permis?
Any other info/experience about this move would be welcome (taxes, healthcare, unemployment protection etc)