Hi
I worked in Paris in the '70's for 8 years or so and have a pension from ARRCO, AGIRC and CNAV. CNAV is the French "State Pension" and you will have contributed to this as well. I claimed mine when I was probably around your age and thought at the time I should have started the process when I was 60 because the official pension age then was 60. Might be 62 now ? I'm 80 so have had a few years of these pensions now.
I would create an account on the AGIRC-ARRCO website - Bienvenue sur le site de l'Agirc Arrco (agirc-arrco.fr) . I think you can apply from there and there are loads of FAQ's. Do the same for CNAV - L'Assurance retraite – La retraite de la Sécurité sociale (lassuranceretraite.fr). Again you cam make your 'demande' from there.
CNAV will go on qualifying years and AGIRC/ARRCO are based on your points. You can see the point value here - https://www.insee.fr/fr/statistiques/serie/010593202 - doesn't seem to go up a lot !
As UK Resident the French will tax you at around 20% flat rate on the whole pension. You declare the pension to HMRC which is added to your total income and taxed, then claim the French tax paid as a credit.
Have been a member on the forum for some 10 years or more but it won't seem to let me re-set my pwd on my original login so created new account !
Hope this helps
Barry