Actually, there were three fronts when the Normandy invasion was completed. Against the Germans, the western Allies were already fighting in Italy in what Churchill called the soft underbelly of Germany, I think, (they captured Rome on June 4, 1944), and the Soviets were already fighting on the Eastern Front before D-Day, as you know. Also, on D-Day, the land forces that landed and parachuted into Normandy were American, British, and Canadian. In fact, it was the Canadians who made the greatest inland advance on that day--9.6 km. There were also about 1000 Australians who participated in the D-Day landings, attached to the Royal Navy directing fire onto the Normandy beaches; flying Spitfire and Typhoon fighter planes against German land fortifications and mobiles on the ground; or as amphibious infantry with the British in order to learn amphibious techniques to be brought back home for further amphibious attacks against the Japanese in the South West Pacific.
The establishment of the Western Front helped to shorten the war in Europe. In fact, Hitler put most of his resources into the Battle of the Bulge to try to split and destroy the American and British Armies on the western front and when that failed, well, the war was lost for the Germans. It's also interesting to note that the Battle of the Bulge was the most costly battle ever in American history--20 000 American lives were lost in that battle.