Greetings! Whilst I am unable to go too much in-depth on the shortcomings of the various French-Allied commanders during the Battle of France and the Low Countries Campaign of the Second World War, you might find this adapted version of a longer deep-dive into the early war performance of the Wehrmacht useful to your question about the Allies being outmatched in terms of manpower and weapons. The general takeaway here (the tl;dr if you will), is that the Allies were not markedly inferior in terms of manpower OR weapons, but they were crucially outmatched in other critical areas, such as a modern air force and a High Command which was more flexible towards on-the-ground changes in the battle:

Against France and Britain in the 1940 campaigns, the Germans were not able to take advantage of numerical or even materiel superiority. The French fielded the equivalent of 91 divisions in the Spring of 1940, and their tanks (namely the H-35, H-39s, and Char-Bs) were in many respects the equivalent (and in some ways better) than the already aging Panzer I and IIs that were still in some of the Panzergruppen. The British for their part, contributed ten infantry divisions in the British Expeditionary Force, which was for the most under equipped and poorly trained.. The Luftwaffe once again outnumbered and outgunned the combined British, French, Belgian, and Dutch air forces and the presence of radio in every element of the now elite Panzer divisions (as opposed to the lack of it in the Anglo-French ones) meant that the Germans had a slight upper edge troop-wise.

The real competence and brilliance of the Wehrmacht in this campaign however (known as Fall Gelb, or Case Yellow), was in choosing where and when to strike*.* You have probably learned from watching WW2 Week by Week about how Manstein’s Panzers bypassed the Maginot Line by way of the Ardennes Forest and surprised the Allied forces, who (some less reputable tertiary sources claim), had not expected such an attack. This final note is egregiously wrong: the Allied planners had already envisioned such an attack through Belgium, and the French high command had discussed in detail their Army’s plans for such a maneuver. General Gamelin, the supreme Allied commander, pushed for what the French called “Plan D”, in which a German attack would be met with a defensive line on the River Dyle from Wavre to Louvain and Antwerp, and then onto a line on the Meuse River from Namur to Sedan.

The Wehrmacht plan consisted of a two-pronged assault involving Army Group A and B (under the command of Gerd von Rundstedt and Feodor von Bock respectively). Army Group A was made the larger army in an insightful decision by Erich von Manstein and Rundstedt (wihich Hitler supported), as this was the group which contained the armoured spearhead of seven Panzer and three motorized divisions (alongside other formations, it totaled some 44 divisions). The Germans achieved surprise with their attack, and the French centralization of Command, as well as general incompetence by its commanders, meant that the campaign progressed with unexpected speed. R.A.C Parker on Fall Gelb:

“In war between comparable forces victory goes to the side which suffers fewer delays and confusions and in which the chain of command is more lucid and effective. The best French troops and their equipment and morale were fully equal to those of the best German troops. They were defeated because too often they were not in the right place at the right time.”

So in addition to its use of armored divisions and rapid maneuvers, the German Army made such short work of the 1939-40 campaigns against roughly equal Allied armies due to its superior command structure; or lack thereof, recall the German Army's doctrinal concept of Auftragstaktik (mission-type tactics), in which the individual soldier was taught how to take their own initiative in battle situations, and placed independence of command on officers without having to constantly seek approval from superiors. Though behind the scenes Hitler had quarreled with many commanders in the lead-up to these campaigns, he could not deny their effectiveness and professional merit by the time Paris had fallen. Competence and brilliance in the Wehrmacht came before blind political loyalty, and the generals who scythed their way through Poland, France, Luxembourg, Belgium, and the Netherlands were exemplary at the former, often making up for their deficiencies in the latter.

There is also however, the political sphere of influence on the poor state of French High Command when the Germans did launch Fall Gelb, many of their senior officers (Gamelin, Weygand, and Petain) were veterans of the First World War who (unlike the Wehrmacht in the interwar years) had not taken part in (or for that matter, actively encouraged) R&D efforts to bring the French Army's tactics up to par with its equipment. There is also, and I highly recommend further reading on this, the argument that due to the political instability and personal agendas of the French Generals, a defeatist attitude emerged as the Wehrmacht progressed deeper into France, which added a new dimension of difficulties to cooperation in the Allied war effort.

Hopefully this response helped somewhat, and feel free to ask any questions about further Wehrmacht successes against the Allies.

Sources

Balsamo, Larry T. "Germany's Armed Forces in the Second World War: Manpower, Armaments, and Supply." The History Teacher 24, no. 3 (1991): 263-77. https://www.jstor.org/stable/494616.

Chant, Christopher. Warfare and the Third Reich. New York: Barnes & Noble Books, 2000.

Holland, James. The War in the West: A New History, The Allies Fight Back 1941-1943. London: Corgi Books, 2016.

Padover, Saul K. "France in Defeat: Causes and Consequences." World Politics 2, no. 3 (1950): 305-37. Accessed February 23, 2021. https://www.jstor.org/stable/2008907.

Parker, Robert Alexander Clarke. The Second World War: A Short History. Oxford: Oxford University Press, 2001.

Porch, Douglas. "Military "Culture" and the Fall of France in 1940: A Review Essay." International Security 24, no. 4 (2000): 157-80. Accessed February 23, 2021. http://www.jstor.org/stable/2539318.