...In his role as overall Commander of Ground Forces, Montgomery was determined to keep attacking on his left to draw in the bulk of German armour; this allowed the American Divisions on his right to capture Cherbourg in the face of lighter resistance, before turning South through Mortain, Le Mans and on to the Seine.

Clearly, the burden of fighting German armour and strong supporting infantry was borne by the British, Canadian and Polish armoured divisions. Moving East against 20 German Infantry divisions with 3 Panzer divisions in the area of Argentan & Chambois. The British XII & XXX Corps, supported by the Canadian II Corps and the Polish 1st Armoured Division succeeded in breaking through.
The battle of the Falaise Gap, 12-21 August, was the decisive engagaement of the Battle for Normandy. Here the 7th and 5th Panzer Armies became encircled by the advancing allies at the town of Falaise. The result was the destruction of the bulk of Germany's forces west of the Seine, and so the route to Paris and the German border was opened. The German Commander surrendered Paris on 25th August, 10 days ahead of the 90 day forecast for the advance from the Normandy beaches.
Between D-Day and crossing the Seine 77 days later, the Allied Armies suffered 209,672 casualties including 36,976 killed in action. In addition, 28,000 air crew were lost in operations over France during the run up to D-Day and in the subsequent battles. More than 40 German divisions had been destroyed with the loss of 450,000 men of whom at least 50,000 were killed.
The liberation of Caen
Caen in ruins
The battle of the Falaise Gap
Germans surrender at Falaise