Retired EU citizen with no access to S1, Part time Resident in France, Is it possible to Obtain a Carte Vitale?

I would like to know how to go about obtaining a health card for France (Carte Vitale), given my particular situation.

My specifics details are:
I am an Irish citizen and have an Irish passport which is currently valid to 2026;
I first received my Irish citizenship via a post-nuptial application in 2003;
I have never lived in Ireland long term so I do not have an Irish medical card nor a permanent address in Ireland;
I am also an Australian citizen (from birth, where I am registered as a resident for tax purposes);
I am currently retired (age 71 years) and divide my time approximately equally between France where I live with my UK partner (who has French residency), and Australia;
I have been registered as a resident with the local village mairie (where my partner owns a house) in France since 2016 ,ie, for 7 years now;
I do not own any property in Ireland or the EU and am not registered as a part owner of my partner's house in France, and as such do not have any house documents (utility bills etc) with my name on them; I also do not have a French social security number;
Up to now I have taken out private health insurance when staying in France/EU;
I have not attempted to obtain a carte vitale French medical card up to the present.
Given the above situation, can you advise me of my rights, and if possible, the means of obtaining a French medical card (carte vitale).