It was a cheap shot, but I couldn't resist it!
However, to be fair, three Free French Squadrons were assigned to No 84 Gp (2ATAF) for D-Day: 329; 340; and 341 Sqns flying Spitfire XIs out of Merston (145 Wing). There was also 346(Fr) Sqn flying Halifax III/IV for No 4 Gp out of Elvington which may have been assigned to Overlord.
Perhaps the modern FAF were on their new national exercise which gives their pilots experience in the realism of warfighting and air combat. Its called "White Flag".