Well, to be honest, all three of those sources are less-than-rigorously-researched popular histories, rather stale, and, frankly, British. Interestingly, one of the best views of the HQ-level of the Battle of France is British---Major-General Sir Edward Spears who was the Cabinet liaison to the French high command. His picture of the dithering of Gort in the crucial days of May is less-than-flattering---see his fascinating ASSIGNMENT TO CATASTROPHE.
Gort's one rather pathetic stab at smashing the German cordon, sending two seriously understrength battalions of infantry tanks with a smattering of infantry nearly did the job---it did frighten the Germans badly before they defeated the push with artillery. If he had mounted a serious counterattack to regain contact with the French south of the cordon, who knows what might have happened.
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