if I understand correctly, your passport (and ESTA ?) have first names 1, 2 & 3, your flight ticket has first name 1 but your EB membership has first name 3.
If yes, you’re lucky to never had problems for crediting flights.
As you rightly said, the rule is that ticket, passport and FFP must match, and I believe AF is applying this.
If I were you, I would contact Eurobonus to correct your 1st name in the program for your 1st first name,