In footage from the time, a US intelligence officer explains the details of the German breakthrough in France.
At dawn on 10 May, the Germans began an invasion of Belgium and the Netherlands. They advanced against France through the Ardennes Forest, which the French had considered to be impassable to tanks. On 11 May the French cavalry retreated over the River Semois; on 13 May the Germans crossed the River Meuse into France at Sedan, aided by waves of dive-bombers.
By 21 May, this thrust had reached the Channel and encircled 35 Allied divisions, including the BEF. Although the French army put up token resistance for several more weeks, their spirit was broken and the German advance south from Belgium was swift and decisive.
For reasons still not clear, Hitler demanded a pause in the fighting, which gave the Allies enough opportunity to evacuate around 340,000 troops from Dunkirk and a further 220,000 from other French ports.
Despite desperate attempts by Winston Churchill to bolster French resolve, the defeat of the British and French armies in May effectively spelled the end of French resistance. The Allied armies, completely unprepared for the rapid, mobile operations of the Germans, had simply been out-fought at every turn.