Strategy for D-Day
Tested in Very Hard/Furious.
When the scenario begins, move all of your movable units to Argentan, Avaranches and Le Havre. Note that there are some in Rotterdam and Amsterdam, and some in southern France. You have to do it quickly or it is going to be too late. Put all planes on air superiority and interdiction missions in Normandy, and hope they don't all get shot down on the first day.
When the first Allied paratroopers arrive in Caen, attack them the moment they land with all of the adjacent troops. Do not bother trying to recapture Caen since the Allied marines will land there soon. When they do, attack them with everything you have. If you are lucky, they will be destroyed and you win easily. However if you are losing the battle, do not be afraid to call off the attack.
The Allies will capture Cherbourg. If they attack your armies in Avaranches, quickly attack the allied troops in Caen. This is important to make sure that they can not attack effectively. Done properly, the garrisons should hold.
After all of the armies have arrieved in Argentan, Avaranches and Le Havre and their org is full (put them into offensive supply mode if the org is low), attack Caen. If the invasion fails, wait until the org is full and attack again and again until Caen falls.
Hold Caen and destroy the remaining allied troops in Cherbourg. Just put enough troops in Caen and other beachheads and strategic victory is just a matter of waiting.