Actually, people who work for the UN get a different type of permit, and many of them (including non-EU citizens) live in France and work in Geneva.
I thought this was just for diplomats; I sort of assumed OP's wife was a "normal" employee and this wouldn't apply.
But maybe he can shed some light on this and say which permit they are actually applying for.
When I worked there, even interns got the permit, and most of the process was managed by HR once people started their contract.
But yes, this is something the OP & his wife should take into account.
Good to know, I really wasn't aware