When the first German units moved westward on 10 May 1940 into Holland, Belgium and Luxembourg, it looked as if Gamelin had been correct in anticipating the enemy's main thrust. The bulk of the BEF and the French 7th and 1st armies moved northeast, as planed, to co-operate with the underequipped Belgian and Dutch armies. But they quickly felt the weight of superior German airpower and the two Panzer and twenty-seven divisions of German Army Group B.
Meanwhile, on 13 May 1940, the main German attack by Army Group A (forty-four divisions) began to the south. Seven Panzer divisions with ample air support struck at the relatively weak French 9th and 2nd armies, reaching and crossing the Meuse river and then breaking out to the west within a matter of days.
It was at this point, as Gamelin and his subordinates sought to respond to tis unexpected drive, that the weakness of the Allied air forces and the slowness and confusion of the command and control system of the ground forces made itself felt. Efforts during 13th-16th May to move three French armoured divisions held in reserve into a position to attack the German flanks collapsed in a muddle of air attacks, conflicting order and inadequate logistical arrangements. The panzers raced on, and by 20th May had reached the sea.
The only hope for the Allied forces was to lunch a major counter-stroke by forces north and south of the German corridor against the exposed flanks of the GErman line of advance before slower German forces could move up to consolidate the gains made. Though an obvious move in theory, and ordered on several occasions in the third and fourth weeks of May, it proved impossible for the Allied commanders to organise effectivley. German command of the skies in combination with the lack of combined arms in the remaining British and French tank formations, along with a crisis of morale in the French High Command (which the replacement of Gamelin by General Maxime Weygand did little to counteract), meant the Allied counterattacks were weak and unco-ordinated. Though they caused momentary alarm to the German Hish Command, hastily mounted attacks by the newly formed French 4th armoured division and then by a British tank brigade at Arras in the fourth week of May, achieved initial success but foundered for want of sufficient infantry and artillery support. With Army Group B continuing to advance and Belgian resistance collapsing, all subsquent efforts to mount a co-ordinated offensive from north and south foundered.
By the last week of May the BEF and the remains of the French 1st army were pinned up against the coast around Dunkirk, and on 26th May orders were given to prepare to evacuate as many men as possible by sea. A certain amount of uncertainty in the German High Command (OKW) over which German units should be primarily responsible for eradicating the Dunkirk pocket, combined with too much reliance on the Luftwaffe (whose bombing could be partially countered by fighters operating from bases across the English Channel) meant that between 27th May and 4 June 338,000 men (140,000 of them French) were successfully taken off by boat from Dunkirk. The 'Miracle of Dunkirk', however, did nothing to alter the fact that France was on the verge of defeat.
Against ninety-five German divisions, including all ten Pnzer divisions, now preparing to sweep south in June, General Weygand could only depoly the remnants of forty-five divisions, only three of which were moblie. The outcome of the battle fought between 5th-9th June along the line of the Somme and Aisne rivers was a foregone conclusion, and once more the Panzers reaced forward.
On 14th June, Paris, now an open city, was occupied by the Germans. For time it seemed as if the French goverment might carry on the fight abroad; but on 16th June the generals and politicians who wanted an end to it all won out over Reynaud and other resisters; and a new leader, Marshal Philippe Pétain, the ageing hero of the First World War, determined to bring both the war and the 'decadent' republic to an end, sought and obtained German terms for an armistice that was signed on 21st June. The Germans continued to occupy and later exploit the northern part of the country, while in the south a new authoritarian regime was created by Pétain at Vichy which in coming years would seek to promote French interests by currying favour with the new masters of Europe.