The Allies had air superiority (as quant_dev commented) is the basic explanation. I'll try to add some details.
First of all, ground support trained pilots were in short supply. Most pilots stationed in France were trained on bomber interception, not close ground support. Pilots/units with this training were usually stationed on the Eastern Front. Training for pilots in general was limited due to shortages of instructors, training aircraft and fuel. Instructors, particularly those in non-interceptor roles, were increasingly assigned to combat units. By the end of 1944, all flight instructors were reassigned to combat units.
German pilot ranks were also decimated by several months of aerial combat against the technologically better P-47 and P-51 fighters and better trained Allied pilots. Over 2000 German fighter pilots had died in combat in 1944 prior to the invasion. This left less experienced pilots for the most part with the job of mounting a defense. They did manage to launch about 100 sorties during the invasion but these were generally ineffective, as you noted.
Adding to this was confusion over the nature of the invasion. As you also noted, German commanders thought that the Normandy invasion was a feint to mask an invasion in the Calais area by Patton's (fictional) First U.S. Army Group. Thus they held their ground and air reserves to meet this perceived threat.
If the strategic bombing of Germany hadn't been as successful, the invasion would have been a much more iffy proposition than it was.