First. I'll dig into the premise. The success of the Normandy invasion was not necessarily to break through to the Seine river, though everybody hoped for it, it was even retaining a foothold in Normandy and attracting there enough German panzer divisions (facing the air and artillery superiority, German tanks and self-propelled guns very the only forces capable to stop the allies, the towed ones were usually very vulnerable to allied artillery). The breakthrough itself was not needed.
On a strictly operational basis, your argument is actually quite sound, and one that I've never seen before, or at least presented so cogently.

That said, it ignores the massive
political consequences of a failed invasion. First, a complete purge of the Allied high command; Not just of army commanders but naval and air as well.
It was no secret that much of the problem for the navy was the insistence of Admiral King in sending his z-class officers to support Overlord, (1) while every admiral who could tie his own shoelaces went to either the Pacific or were off sinking the ever shrinking number of U-Boats.
1) The American admiral Kirk was referred to by Eisenhower as "...absolutely the worst admiral I had ever met in my life!"
No complaints about the strategic air forces of the US or the tactical air forces of the RAF in Normandy, but Bomber Harris' obsession with terror bombing and the USAAF fighter pilots with thinking that WWII could be won by shooting down the most Luftwaffe fighters...
Another consequence would be the probably fall of the Churchill Government and the leadership vacuum he would leave behind. There really isn't anyone to effectively replace him as a war leader except the socialist Ernest Bevin, and he would represent a member of a minority party, albeit in a national government.
Note: Despite what others have suggested in countless threads, FDR has no chance of losing in 1944, short of a stroke, and he had a cerebral hemorrhage, not the same thing. Whenever FDR goes, he goes. His brain is a ticking time bomb, but with a set timer, not as you might see with a stroke caused by stress.
Stalin OTOH will be furious. Whether he delays Bagration is anybody's guess, but he did order it when it best suited him. So even a failed Overlord is likely not to see any German forces sent east again anytime soon. But you could see ITTL at the very least the Soviets overrunning all of Austria, Czechoslovakia, Germany up to the Elbe, parts of Central Germany and even Denmark!

Unless Hitler sends more forces east than OTL, easing the western front. Butterflies, butterflies, butterflies.
With that happening, the situation would be resolved by the southern France invasion, perhaps strengthened by 3-4 more divisions brought in from Britain, rather than used in congested Normandy. In OTL the southern France was, by August 1944, left without panzer divisions. Both 9th wehrmacht and 2nd SS, as well the 17th panzer grenadiers were withdrawn to Normandy and if this scenario was repeated in the ATL, there would be nothing to stop the southern French invasion.
But if Overlord is defeated, what is to prevent the Germans from redeploying to the South of France? Besides, the terrain of that region is the worst in all of France, leaving only one advance route to the north free of rough terrain. If I were in command of a mostly motorized infantry force, I would not be sanguine at the prospects of fighting my way out of there. You don't really break out into open terrain in Southern France until you are all the way up to Vichy, by which time the front will have become so large and the German supply lines so extended and vulnerable that the Germans will have been forced to evacuate to Alsace-Lorraine anyway.
By October 1944 the German army would have to withdraw at least to the Seine line anyway.
I'm confused.

You seem to be describing not an out-an-out Overlord defeat, but some kind of extended period of front isolation as might have been expected in a 1943 Roundup invasion...?
The conclusion is that even a very modest success of Normandy landings, e.g. in the form of only 3 our of 5 invasion beaches secured, would do the job. With the naval artillery advantage, the loads of tanks and anti tank towed guns and carpet bombing I don't think Germans could do much afterwards.
Failure of 2 out of 5 landings is still likely to cost Ike and Monty their jobs.
But now back to your premise, i.e. complete defeat in Normandy. The allies would have a problem.
The August southern France invasion would probably be opposed by at least two panzer divisions. However, the Germans would not be able to send much reinforcement to the south because they would have to face a possible repeat of a cross-channel invasion. If the roughly 12 allied divisions (there were eight of them in the Dragoon operation, however, with the southern France invasion now being so vital they would likely be reinforced from Britain by a few more) managed to keep a foothold in the south of France, they could be reinforced by some 4-8 divisions arriving monthly from Britain and the US.
Problems for the Allies:
Much longer supply lines and LOCs to Dragoon. Greater redeployment time. Little in the way of air support compared to Overlord. Rough terrain.
Pluses for the Allies:
New Supreme Commander, likely to be Alexander. Brooke's negative opinions of the man will hold little weight now. Devers is likely to be the commander of an expanded Dragoon, and Ike's negative opinion of him will hold little weight now.
Whether or not they would themselves manage to cause Germans to withdraw from to the Seine line or even further or whether another cross-channel invasion would have to be carried out (this time better prepared and against much weaker opposition) I can't say, but Germans would eventually have to withdraw from France anyway, probably before the end of 1944.
The probable massive loss in landing craft will cripple any further landing operations in Europe in 1944, and could even hurt Dragoon. And Hitler once again is the problem. He had a very bullying personality. Sending frex an entire SS panzer division (2nd/Das Reich) off for weeks haring about to-and-fro through Southern and Central France hunting down a few hundred marquis and slaughtering hundreds more civilians all in the name of installing fear in the civilian populace and avenging the assassinations of less senior SS officers than you could count on the fingers of one hand!
Consider Hitler's reaction to the news of an escape by some 50+ Allied PoWs, or any uprisings by any civilians in areas of German control.
Christ, even as the US Army was closing in on Munich in 1945 from three different directions, and the city was hit by a small anti-Nazi uprising by a few Wehrmacht units, the local SS and pro-Nazi Wehrmacht units
abandoned the front to concentrate their forces in attempts to "crush the traitorous rebels". You saw the comical sight of loyal nazi troops attacking Wehrmacht barracks even as US troops were attacking them from the rear!
Something similar happened at Dachau, where the SS guards opened up with machine guns on the prisoners AFTER the US troops arrived on scene. Funny thing was, after the SS guards surrendered, they all tried to escape!


Apparently they didn't realize that the Americans were crack shots!

IOW, the lesson was: Nazis like to fight the battles that they can win, not the battles that they must fight regardless of "victory".
Or possibly any other scenario
How about a scenario where Hitler abandons the entirety of Nazi-occupied Europe and sends everything down to the last guard dog, luger, and army pastry chef to either Yugoslavia (to fight Tito), Italy, the South of France, and the beaches of Normandy, Brittany, and the Pas-de-Calais?

What are Overlord's and Dragoon's chances then?
