Belgium had remained officially neutral prior to the German invasion hoping that the neutrality would allow it to stay out of the war. Despite their hopes they knew was more than likely that the Germans would invade France through Belgium, so officially there was no coordination between the French and Belgiums.
On the morning of May 10th the Germans began their assault on Belgium and France. They began by landing gliders in Belgium forts and bridges near the border, successfully capturing many of them. By May 11th the Belgium armies front broke and they retreated to the Dyle Line. As the Belgium forces fell back to the line, the British and French forces began to arrive. While on paper the British and French armies were as large as the German army they faced, and in fact some of the French tanks were actually superior to the German tanks, the Allied tactics lagged behind the Germans who had learned to successfully coordinate their land forces with their air force. In addition German tanks were equipped with radios and thus were much more maneuverable .
On May 14th the French launched an armored counterattack against the German Panzers, the attack was tactically successful but the French did not have the forces to follow through or continue the attack so they withdrew.
Meanwhile to the South the Germans had successfully crossed the Ardennes Forest with armor. The French had not believed it was possible to do so in force and thus this part of its lines was poorly defended, with few anti tank or anti aircraft guns available. The German forces quickly reached the Meuse River at Sedan and under cover of massive air support made a successful crossing of the river. Within a day the German tanks were in open country moving toward the Channel almost unopposed. The French army was now cut in half and the British forces were in also now nearly surrounded. The Germans by May 22nd had effectively won the battle of the west.