- Theatre: North West Europe
- Dates: 10 May 1940 to 22 June 1940
- Location: France, Belgium and the Netherlands
- Outcome: German victory in Holland, Belgium and France, leading to an occupation that would last over four years and a desperate British evacuation from Dunkirk that left the UK facing invasion.
- France: General Huntziger's 2nd Army and General Corap's 9th Army (around 12 infantry and four horsed cavalry divisions)
- Netherlands: Ten divisions and the equivalent of ten more in smaller formations
- Britain: Viscount Gort's British Expeditionary Force (BEF) comprising 13 divisions of infantry
- Germany: Army Group A, under Lieutenant General Rundstedt and comprising the 4th, 12th and 16th Armies, plus two armoured groups, totalling 44 divisions; Army Group B, under General Bock, comprising the 18th and 6th Armies (including three armoured divisions)
Although Hitler's armies were smaller than those of his opponents, the Germans had both air superiority and imagination. More than half of France's 800,000 troops were confined to manning the defensive Maginot Line, a line of fortifications facing Germany from the Swiss to the Belgian frontiers. The Germans simply sidestepped them.
On 10 May 1940, German forces advanced into neutral Holland, with parachutists capturing strategic bridges and landing at airfields around The Hague. By 12 May, German forces were on the outskirts of Rotterdam, and Holland surrendered on 14 May.
In Belgium, German airborne troops landed on 10 May and the Belgian front was broken the next day. German tanks rolled west and the Belgians retreated to the Dyle Line, which ran from the Franco-Belgian border in the south to the River Maas in the Netherlands. Although this was reinforced by French and British divisions, it was abandoned on 15 May, and Belgium sued for peace on 27 May.
The Germans 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.
The narrow breach this created widened rapidly, allowing General Heinz Guderian's German tanks to pour through. They crossed the River Oise on 17 May and reached Abbeville, near the Channel coast, on 20 May, cutting off the Allied armies in Belgium.
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.
By late 1940 he had developed his strategy - it was simply a matter of time, as far as he was concerned, before the Allied powers were defeated.
On 5 June, the Germans began a new offensive from their positions on the Somme. After two days of fierce fighting, their tanks, led by Rommel, broke through toward Rouen; on 9 June they crossed the Seine. The same day, the Germans attacked on the Aisne and eventually turned towards Switzerland, cutting off all the French forces still holding the Maginot Line.
On 12 June, General Maxime Weygand, the French commander, told the French premier Paul Reynaud that the battle for France was lost and that a cessation of hostilities was the only option.
Reynaud's government was divided between surrender and resistance, but faced Germany's inexorable advance through Paris and into the Rhône Valley. On 16 June Reynaud resigned and a new government was formed by Marshal Philippe Pétain, the hero of the Battle of Verdun during World War 1.
Pétain immediately requested an armistice. On 22 June the new Franco-German Armistice was signed at Rethondes, in the same railway carriage where a humiliated Germany had signed the Armistice of 1918. France was divided into two zones: northern France was to be occupied by Germany, while the south east was to remain under the control of Pétain's Vichy-based government.