Does EES apply to people with 12-month visiteur residency cards?

You should be able to bypass the EES by showing your cards

We are retired Americans with a second home in France. Every year, we obtain an annual 12-month visiteur carte de séjour (now in year five). 

While our tax home is the US, we are registered in the French tax system, file French tax returns based on our US income, pay taxe foncière and d’habitation and belong to the Assurance Maladie for healthcare. We rotate physical residency every six months or so. Will EES apply to us? 

EES is not intended to apply to people with long-stay visas or French residency cards, which extend a visa after people settle in France, so people with a ‘visiteur’ residency card should not be concerned.

You should be able to bypass the EES by showing your cards. 

The same will also apply to people with fixed-term ‘temporary’ long-stay visas for France, which are not renewable with a residency card. 

Note, however, that non-EU citizens with French residency cards are meant to abide by the 90/180 days rule with regard to travel in the EU outside of France (although they are not subject to EES, and you are unlikely to be subject to checks on this due to the lack of borders within the Schengen area). 

However, you may wish to consult an immigration and/or tax lawyer to clarify your situation generally, as the residency and tax set-up you describe appears to be a mixture of features usually associated with either French full-time residents or non-residents.