One could argue that what really decided Normandy's fate, and the fate of all of occupied France, was Operation Bagration, the real gut-punch that smashed the Wehrmacht and broke them, hundreds of miles to the east.
The scale and savagery of war on the eastern front is so mind boggingly incomprehensible, and relatively unknown for an English-speaking audience. If you have not, I highly recommend Dan Carlin's Ghosts of the Ostfront series of podcasts, to get even a sense of the insanity.
The western front was, in totality, almost a sideshow in comparison to the titanic, inhuman struggle raging from Black to Baltic seas.