The requirement is, in fact, that if the proposed itinerary involves more than one Schengen country, the visa should be issued by the country that is the "main destination". Only if there is no "main destination" is the country of first entry to the Schengen area the country that should be applied to.

So, if your friend is arriving in France and travelling from there to Italy and will be spending a reasonable amount of time in Italy (i.e. not just passing through and then flying out, for example), then there should be no problem. (In practice, it's probably not so rigid as the rules suggest anyway.)

I would add, though, that anecdotally French consulates/embassies around the world are better organised and less hide-bound about the minutiae of the regulations than most other Schengen countries when it comes to issuing visitor visas, but if they have no appointments then Italy it might have to be!