In 1939-40, 45% of the army was at least 40 years old, and 50% of all the soldiers had just a few weeks training.^[60] Contrary to what the blitzkrieg legend suggests, the German Army was not fully motorised. Just 10% of the Army was motorised in 1940 and could muster only 120,000 vehicles, compared to the 300,000 of the French Army. The British also had an "enviable" contingent of motorised forces.^[60] Most of the German logistical tail consisted of horse-drawn vehicles.^[61]

Only 50% of the German divisions available in 1940 were combat ready,^[60] often being more poorly equipped than their equivalents in the British and French Armies, or even as well as the German Army of 1914.^[62] In the spring of 1940, the German army was semi-modern. A small number of the best-equipped and "elite divisions were offset by many second and third rate divisions".^[62]

In other words, Germany's army at the time was to a significant part a Potemkin army. If the Allies didn't know that, it's no wonder that they were afraid, especially seeing that they themselves had poorly equipped divisions, too. The situation was reversed for German military leaders, who originally only wanted to delay an all-out confrontation on the Western Front until 1942 when they could arm themselves in turn.

This (fairly well-referenced) Wikipedia article also points out that the Blitzkrieg narrative was created after the fact, that is, the invasion was more successful and victory more decisive than planned. From what I gather, the key factors were the use of communication by the (otherwise inferior) German motorised forces, and the French leadership's mistaken expectation of an attack focused on the Belgian-Dutch border (a more southerly attack cut up their lines).

_{*Lunatic*, n.
One whose delusions are out of fashion.}