Historiography of the campaign in the West
The first plan for the strike against France, a rehash of the Schlieffen Plan, had, by the last week of February, been replaced with von Manstein’s conception of squeezing the Allies between the sea and a main thrust from the Ardennes to the sea.
Once applied in May, its results are well known. Against an opponent with slight superiority in men and equipment, the Heer won with amazing speed and small casualties. Finesse and movement defined the moment, not the grinding attrition of the trenches. This was baffling to all witnesses. This miraculous event demanded an explanation, and several were made in succession. They were marked by the clash of two ways to interpret history, materialism and voluntarism. In this context they mean whether the campaign should be understood as the result of the war economy, equipment, force disposition, etc. or military willpower.

The voluntarist thesis was laid out in the post-battle propaganda. It emphasized Allied material strength, showing their impressive fortifications and tanks. This was counterposed on the German side with the superior valor of soldiers and brilliance of commanders, which surmounted material gridlock to achieve a “triumph of the will”. Overwhelming success in the West was seen as a confirmation of National Socialism’s strongly voluntarist outlook.
The materialist antithesis came with the first generation of historians. They claimed that, despite equal numbers, Germany had the right weapons. Having predicted it couldn’t win superior numbers nor a lengthy war, its leadership sought years in advance a “strategic synthesis” between the armaments economy -producing tanks, trucks, etc.- and a new military doctrine of using those new weapons for encirclement maneuvers, speed and immediate victory.
Critical historians, however, realized this was wrong. German rearmament did not fit into the concept of Blitzkrieg, neither before the war nor up to July ’40 when the main priority was ammunition, particularly for the artillery. This, and the first plans for a full frontal attack, shows Berlin’s expectations were close to the mass battles of the Great War. Von Manstein merely came up with a last minute “military fix”. Early German depictions are more accurate than those of the following historians.

Tooze, however, notes some caveats. At the heart of von Manstein’s plan were not revolutionary new ideas of mechanized warfare but an ancient principle: victory by superior concentration at a decisive point. Whereas the Allies distributed their forces equally along the front, Germany had a skeleton garrison in the Westwall, a modest offensive force in the Netherlands and the best units and bulk of its strength on the Ardennes. There, a superiority of almost 3:1 was achieved. Germany had more numbers, not on the whole front but exactly where they mattered. This was made possible by mobility and fooling the enemy, which disregarded the Ardennes and moved to counter the lesser Dutch offensive.
Allied foolishness, too, played a large part. The plan was a risky gamble. Overwhelming success would not have been achieved if the main thrust had been counterattacked and/or less forces moved to the Netherlands. The massive force concentration on the Ardennes was highly vulnerable to air attack and this was only prevented by overcommitting the Luftwaffe, leading to a high rate of casualties that made itself felt later over Britain.
Simple geography was in Germany’s favor. The sea itself played the role of a pincer in the encirclement maneuver. And it was close to the German border on good roads. The vast, poorly developed Russian plains would prove far harder to tame.
So willpower only succeeded because it was given good material conditions.

One footnote: French tanks being dispersed across divisions, compared to Germans having them in only a few, are not very relevant. France had more tanks and could afford to do that. It still had powerful dedicated armored divisions of its own.