The French were in no position to decline German demands. Germany would not have lost too many troops capturing the remainders of the French army in south France, anyways... Germany only lost about 160,000 troops in the battle of France. France lost twice that.
Furthermore, compare that to the number of German deaths on the Eastern Front by 1943: nearly 3 million.
Don´t play with numbers, German army in 1944 was larger than it was in 1939. To say it other way, after German had suffered 3 million losses, their army still kept increasing in size. Numbers alone are meaningless.
Thing is, in Battle of France you might have lost for example Erwin Rommel. Or some other high ranking German officers. And they certainly were important for outcome of the war, even if they alone could not change it. Suddenly, 1 loss becomes more important than 10 000. And again, maybe if Italians would have kept suffering more losses, somebody might have realised needs for improvements, and maybe that someone would have magically been able to convince Mussolini about fact that their army needed improvements before any new offensives.
Maybe after 50 000 losses more without victory, Italian soldiers might have went on strike or something. Maybe Mussolini would have noticed that and realised something he did not historically.
Anyway, not a big deal necessarily. But hey, who is to say British had so small army in alternate history, maybe in alternate history they would have decided to triple size of their expeditionary forces. With trice as much soldiers in France, what would have happened to German invasion, that at so many points could have went horribly wrong.
The big point is: I am not saying it would have changed something. I am saying, it could have changed something dramatically.