German morale was reasonably good at Normandy at first albeit there was a pretty terrible bombing raid on Caen and massed tank formations east of the town. Many of the coastal divisions were not German at all but other nationalities recruited to the Wehrmacht. Amongst those morale was perhaps low. My father was at Arromanches and he witnessed German prisoners interrogated then executed on LCH-187.
General orders were given ahead of the landings not to take prisoners. Some weeks later there was an awful slaughter in the Falaise gap as German units found American forces had worked around their western flanks and behind them.