The Germans did have a real air force on D-Day. In fact, they even sent some early jets over to recon the landings. What the Germans didnt have was numbers and fuel and theyd lost many of their best pilots - but not all. Their fighters were not able to sortie in amounts that could punch through and hold open a route through the horde of Allied fighters to decisively strike Allied forces on the beach or support their counterattacking Panzers. Part of the success of the Allied landings was paid for in the blood of the fighter pilots who died to keep German air power off the ground troops and the blood of the bomber crews flying support missions and serving as targets the Luftwaffe had to prioritize - thus allowing Allied fighters to kill their counterparts.
Even though the Luftwaffe had been pounded into a shadow of its former self, it was still nothing to sneer at and it was anything but easy for our airmen. Read more here: https://www.ibiblio.org/hyperwar/AAF/AAF-H-DDay/index.html
In addition, after the war the French tried to remove the bunkers from the cliff line at Normandy and were unable to do so. They eventually decided they would leave them as a reminder of what they faced during WWII. Of course, all of us who were not born during the war are grateful they were not able to remove them. Seeing the bunkers in person is extremely sobering.