Since we are free today to consider the possibilities, suppose the United States had a standing army, air force, and the means to ship them to Europe, here is where England becomes critical.
First, let's look at the ramifications of a Europe without a free England. If the fall of France was a disaster since it meant the abandonment of the continent by allied forces, the loss of England would have been even more critical. Right after the fall of England, Germany would be free to sweep into north Africa and finish up routing out defending forces. Italy then could be tasked with watching the borders of the Third Reich while Hitler would be free to shift his might to the invasion of Russia.
Remember, the United States would have likely still been waiting to see what would happen at this point. With the full might of the German army pushing into Russia, the only unknown would be whether Japan would still attack Pearl Harbor, or if Hitler could convince them that the bigger picture would eventually get them what they want and more. Japan would have to concentrate on finishing their campaign in China in order to push into Russia from the east. Or, Japan would be tasked with holding while Germany finished Russia.
There are plenty of possibilities and they hinge on many events. Instead of continuing down this path, let me get to what can accurately be surmised with the fall of England IF the United States were someone ready to attack Germany.
Without English bases, the United States would have had to ship forces to somewhere in Africa without the protection of the Royal Navy and Royal Air Force during long Atlantic crossings. Without England, launching an assault on France would have been impossible, so the U.S. would have to settle for creating a single front in Europe, likely coming in Italy. Before Italy, Africa would have to be secured, before Africa, the Atlantic.
So now, you see the problem.
Another tangent: Perhaps the United States would have had to work its way from the Pacific, battling Japan across the ocean, through south east Asia, and into China. Joining forces with China they would attempt to retake Russia who likely will have fallen to the concentrated - and undivided - German might. But then, what difference would hundreds of thousands of Russian and Ukrainian soldiers conscripted into the German army make for a land campaign. Have no doubt, fighting a war in Russia is a bad idea for anyone, including the 'good' guys.
No, more than likely, if England had fallen, the United States would have had to enter into treaty with Germany. An uneasy piece while we (or they) develop nuclear weapons. But then, if we had the bomb, where would we use it? On Paris? On London?
With the stakes set, enter the Supermarine Spitfire.