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Battles for Luxembourg, the Netherlands, Belgium and France

In May 1940, the Germans launched the Battle of France. The Western Allies (primarily the French, Belgian and British land forces) soon collapsed under the onslaught of the so-called " blitzkrieg " strategy. Following the German breakthrough at Sedan, the BEF, along with the best of the French and Belgian armies, became trapped in Flanders. With the use of paratroopers and concentrated firepower, the Belgian and Dutch armies surrendered after several days. Luxembourg fell within the first day.

The majority of the British and elements of the French forces escaped at Dunkirk. This was due to the combined factors of poor weather, Germans mishaps, and the incredible number of British civilian ships assembled for the undertaking. Following the conclusion of events at Dunkirk on June 4, the Wehrmacht commenced Fall Rot, an offensive against the remaining French armies. With most of the French armies either destroyed or taken prisoner, the Germans quickly broke through the French lines, taking Paris on June 14. As France was falling, the British began the strategic withdrawal of all remaining British troops from France, via French ports still under Allied control.

With the war all but decided, Italy also declared war on the UK and France, but made little progress. With the situation becoming dire, French Prime Minister Philippe Pétain signed the Second Armistice of Compiègne on June 22, 1940, with its terms taking effect on the 25th of June. The terms of the armistice called for the occupation of Northern France, along with the annexation of Alsace-Lorraine into the German Reich. Italy also was allowed a small occupation zone in the southeast. France was allowed to continue its existence in the form of Vichy France, a rump state of the former French Republic, led by Philippe Pétain. The Vichy regime was allowed to keep their colonial empire and navy, as some of Hitler's few concessions.

In six weeks of fighting, the combined allied armies suffered more than 375,000 killed or wounded, as well as 1,800,000 soldiers becoming prisoners of war. Meanwhile, Germany suffered a more modest 43,110 killed and 111,000 wounded. Hitler had expected a million men to die in the conquest of France. Remarkedly low casualties and France's quick defeat led to a massive rise in morale among the German people. With the fighting ended, the Germans began to consider ways of resolving the question of how to deal with Britain. If the British refused to agree to a peace treaty, one option was to invade. However, Nazi Germany's Kriegsmarine, had suffered serious losses in Norway, and in order to even consider an amphibious landing, Germany's Air Force (the Luftwaffe) had to first gain air superiority or air supremacy.