I just finished William Shirer's Berlin Diary after having read his Rise And Fall of The Third Reich a few years ago, which I also recommend (with the small asterisk of both being history recorded by a journalist without any claims of omniscience and an unapologetic product of his time and culture.)
Diary covers 1934 to 1941, so Poland is conquered and divided. France is getting divided up into occupied and Vichy France, England's navy has been somewhat busy, but otherwise hasn't done much, Italy is going out of its way to appear relevant, and Hitler and Stalin are allies.
9/10 of the book are about what you would expect, just with much more detail.
Here's the novel part where I would like your opinions - Shirer asserts that France's shameful military performance is due to three forces.
(1) Their enlisted men are seduced by communism, and thus have their orders from Stalin to not fight.
(2) the elite leadership is secretly, or brazenly fascist. They do not want German hegemony, but a Franco-like strong man of their own is more desirable than democratic chaos. Hence, they do not try that hard to fight.
(3) General cultural decay has infected all of French culture - a general lack of 'moral fiber' that Johnny American has is missing, hence the half-hearted capacity for self defense.
I can see #3 as Shirer being snarky or frustrated and not thinking deeply enough, but #1 and 2 have, to use one of his favorite phrases, "the ring of truth."
EDIT - I just remembered one more rather big deal. He characterized French generals as mostly elderly, having no new thoughts in 20 years, and taking no physical exercise in 10 years. They were sort of professors emeriti of their military. German generals were a sharp contrast - in their 40's or 50's, largely physically fit, and generally very capable. Also a true generalization? I'm thinking their experience in Czechoslovakia and Poland vs. French experience 25 years in the past would make this true, as a generalization?
The general historical consensus on Shirer is that while he's readable, his historical analyses and judgements are quite faulty.
The first point illustrates more of the anticommunist precepts often common within American elite circles and overestimates the importance of Stalin and the Comintern influence upon French Communists. The Molotov-Ribbentrop Pact created a great deal of confusion for the non-Soviet left and France was no exception. Stali lost an inordinate amount of prestige in his pact with Communism's nemesis and would only regain it during Barbarossa. The French Communist Party was outlawed in September 1939, but French Generals frequently would blame their misfortunes in 1940 upon Communist betrayals from within. For example, General Lafontaine attributed his unit's (the 55th Infantry Division) collapse due to a Communist fifth column, but the division's "organized panic" had more to do with its poor training and deployment. The only area where there was a sizable Communist subterfuge was in French industry, where some labor activists like Roger Rambard sabotaged military equipment. These tales found a wider audience in the later Cold War environment and magnified their scale and importance.
Shirer's second point is grossly misleading and absurd in many respects. Sympathy for fascism doesn't translate into lackadaisical poor generalship. While there were many archconservatives within the French military leadership, it stands to follow that a military victory would be the best way to rekindle French national spirit. The fact is that many French generals fought quite hard in the 1940 campaign, but were frequently out of position and hobbled with a doctrine and a command structure that did not allow them to seize the initiative as the debacle unfolded.
As the OP noted, Shirer is engaging in a snarky American nationalism, but I would also add Shirer is recapitulating a Vichy era discourse about the problems with the Third Republic and the correlation between decadence and defeat. The French did suffer an extreme amount of casualties and in places fought very hard. One German veteran of the Battle of Sedan compared the French tenacity st the village of Stonne thus: there are three battles I can never forget: Stonne, Stalingrad and Monte Cassino.
The edit point has some validity in that the French leadership was very much a prisoner of its own doctrinal and strategic assumptions. They assumed that the best way to meet a German invasion was through a methodical counterattack, so they assumed they would have time to do so, which Guderian's panzers did not give them. Moreover, the French lacked radios and communications to make such a massive coordinated counterattack possible. But keep in mind many of these problems were mirrored within the Wehrmacht. Gamelin and von Rundstedt were roughly the same age and both Hoth and Guderian were slightly older than de Gaulle. OKH and OKW had significant reservations about Manstein's plans and constantly tried to reel the panzer drive in when it had gotten started. Rommel actually turned 7th Panzer's radios off at one point during his drive to the Channel so he would never receive an order to stop.
In the end, Fall Gelb was a risky gamble that paid off handsomely. The French had problems, but then so to did the Germans. Attributing defeat solely to cultural and political decay obscures the actual military factors behind French defeat.
Sources
Citino, Robert Michael. The German Way of War: From the Thirty Years' War to the Third Reich. Lawrence, Kan: University Press of Kansas, 2005.
Frieser, Karl-Heinz, and John T. Greenwood. The Blitzkrieg legend: the 1940 campaign in the West. Annapolis, Md: Naval Institute Press, 2005.
Murray, Williamson, and Allan Reed Millett. A War to Be Won: Fighting the Second World War. Cambridge, Mass: Belknap Press of Harvard University Press, 2000.
To call France's contribution a poor showing is a little strong. They were unprepared and overrun by Germany at the start of the war and were forced to surrender. Britain was unprepared too, forced to evacuate from Dunkirk, but then had the English Channel to keep the Germans out.
Nevertheless, after a mediocre showing in N Africa, the Free French fought well enough in subsequent campaigns. An example would be Italy in the weeks leading up to D-Day where General Juin led his troops well and contributed strongly as part of the offensive joined the beachhead at Anzio up with the rest of the Fifth Army, broke the Caesar Line and resulted in the liberation of Rome.
A poor showing? Except for the Fall of France, where did else did the French show this? Were they not fighting beside the other allies from the very beginning to the very end? The Fall of France has many reasons but it was above all poor leadership from French upper command and a good plan combined with a bit of luck by the Germans. You should read the Fall of the Third Republic that's also by William L. Shirer, it's a great book that gives a very clear and complete image.