The invasion of France began of May 10, 1940 while Germany began invasions in the Netherlands, Luxembourg and Belgium. Hitler turned his more of his attention towards the west after his German conquest in Poland in 1939. His goal was to invade the low countries, one of them being France (others are the Netherlands, Luxembourg and Belgium.)
Even though the German Army was outnumbered by the allies, they still moved with extreme effectiveness. They eventually invaded the Low countries, the French army and the British Expeditionary Force (BEF). All of this helped moved German ahead. New offensives were launched at Paris,France and the BEF failed to do justice. The country was now divided into Germany Occupation zones and Vichy France. Germanys next goal was to knock Britain out of the war.
At the time, Frances technology was more advanced than those of Germany, how could have this invasion occurred? Before the invasion, some of the German military leaders even doubted their successes stating that it was a bad idea to invade France. Even Hitler expressed disbelief in his victories. The main reason for Frances' downfall was due to "mistaken assumptions about how the invasion would carry out." <World War II (1939-1945,) Spark Notes>