An Allied loss at D-Day was possible, if not too likely given the superior amount of materiel the Allies poured into it.

So I'm off to talk about a situation where the Allies had indeed been thrown into the sea.

That woud likely have been the worst possible scenario for Europe.
Germany would still be in serious trouble. The Allies would not come running to the table over such a defeat. They would retreat and plan for new operations.
But those operations would take time, and until then only the planned ones could be carried off, if not too securely.

So we have a huge Allied army still sitting in England, just edging to get over the little stretch of water. This would force Germany to keep the garrisons in France in place. Of course some more mobile units could be transported to the east, but they would be far from enough to halt the Russians. A few divisions might even get sent to Italy, bogging the Allies down once more.
But ultimately Germany would still lose, but this time she would basically only lose to the Soviet Union, which due to the transfer of troops (and lack of the opposite later) would suffer more losses, and would feel a right to all of Europe if not just a much larger share than they got historically.

Personally that would mean I would have been speaking Russian as my second language rather than English (it was damn close even in the historical events).