Frontaliers are not required to have a Swiss driving licence for non-professional categories (e.g. A and B), as by definition they cannot have their principal civil domicile in Switzerland (but residence definitions may be different for other purposes, e.g. fiscal domicile, health insurances etc.).
The frontalier authorization G is not a residence authorization (it is distinct from autorisation de séjour, de courte séjour, et d'établissment), although the authorization is inscribed on a residence permit document.
You do not, for example, have the right to become a permanent resident (with a settlement permit C) of Switzerland, no matter how long you have worked for a Swiss company with a G permit.
Nonetheless, a frontalier may have a secondary residence in Switzerland, but they must return to their foreign domicile at least once a week. For those who have a weekly residence in Switzerland (frontaliers semainiers), the regulations define their domicile as that of their family:
Est réputé domicile du résident à la semaine le domicile de sa famille s’il y retourne régulièrement deux fois par mois en moyenne.
Consistent with the general definition of the civil domicile, the provision is destined to make the domicile for driving licensing purposes the one where they have the intention to return to.
In any case, if you will drive a Swiss-registered motor vehicle professionally (requiring categories C/C1, D/D1, or passenger transport authorizations), you require a Swiss driving licence following Swiss rules (e.g. medical exams).
The rules for foreign vehicles themselves are different. For customs purposes as well, frontaliers (daily or weekly) are not considered Swiss residents. You may not use a foreign-registered car for any professional purposes (e.g. driving inside Switzerland to meet with clients). You also need to obtain a customs clearance or authorization if you use your car in Switzerland for more than six months within a one-year period.