Yhyjyk

Residents of France who hold a non-EU, non-EEA license to drive may continue to use that license for up to one year after establishing residency, subject to certain conditions.

The relevant law may be found at www.legifrance.gouv.fr. A more user-friendly account of the rules is available at www.service-public.fr.

The definition of "residency" seems to cover any stay longer than 90 days, which is the time by which a non-EU, non-EEA spouse of an EU citizen must apply for a residence permit.

Consider now the case of a non-EU spouse of an EU (not French) citizen. They reside in the non-EU country for 8 months each year. When they arrive in France for a 4-month stay, they apply for a residence permit for the non-EU spouse. They leave, and six months later, the residence permit becomes invalid.

Does the invalidity of the residence permit cause the 12-month driver's license clock to reset, making it legal to continue to drive using the foreign license during subsequent periods of temporary residence in France?

Citations to specific provisions of French law will be helpful.

Summary: Your scenario does in fact work, but there's no clock to reset.

The second paragraph of R222-1 which you cite (my emphasis):

Dans le cas où ce permis a été délivré en échange d'un permis de conduire d'un Etat n'appartenant pas à l'Union européenne ou à l'Espace économique européen et avec lequel la France n'a pas conclu d'accord de réciprocité en ce domaine, il n'est reconnu que pendant un délai d'un an après l'acquisition de la résidence normale en France de son titulaire.

Roughly translated,

Where this licence has been issued in exchange for a driving licence from a non-European Union or non-European Economic Area country with which France has not concluded a reprocicity agreement in this domain, it is only recognized for a period of one year after the acquisition of normal residency in France by the holder.

Résidence normale has a specific definition given in R221-1 III, which is residing in a country for at least 185 days. Confusingly, this definition is not related to the residency permit (carte de séjour) which is where you get your 90 days from. However, if one were to gain résidence normale, the start date of the one year period is considered to be the date of issue of the first residency permit as per this 2012-01-12 administrative decree Article 4 II.B. Still with me?

In your scenario though, the couple never gains résidence normale and so the one year clock never starts. The couple can continue their 8-months away / 4-months in France ad nauseam infinitum.

For more info, Titles 1-2 of the administrative decree is the most detailed resource I was able to find on the topic.

Please take this answer avec des pincettes as it took awhile for me to sort out the intricacies and I'm not quite 100% sure I got all the details right.