In 1939 the French based all of their defenses on static fortifications. In other words they were preparing to fight WW1 over again. They were not prepared for the mobility of the German blitzkrieg. A fortification is useless if you can get around it, and the Germans did that by attacking through The Netherlands and Belgium something the French did not consider. Where they did give battle they were hopelessly outclassed. It was not fair to say they did not fight hard to repel the invasion, they were simply overwhelmed.
However, when the armistice was signed in June 1940 over 70% of the French armed forces were still intact and for the most part they meekly obeyed the order to cease fire. And of course there is the despicable Vichy faction who surrendered without firing a shot. And worse they began to actively aid the Germans.
I can not imagine a US military that is 70% intact to stop fighting an invader simply because Washington DC fell and a President was forced to capitulate. It would never happen. American history has many examples of our tenacity in war. At the Alamo they fought to the last man rather than surrender. At Wake Island every single able defender died fighting off the Japanese despite numerous calls to surrender. When the Corregidor fell and Wainwright ordered all US forces in the P.I. to surrender most went into the hills to fight as guerrillas. During the revolution the Continental Navy fought the Battle of Valcour Island literally to the last ship to prevent or delay a British landing in North Carolina that may have won the war for Britain. The 101st Airborne was totally surrounded at Bastogne and outnumbered 10 to 1 by the Germans. When asked to surrender and save his men Gen McAuliffe answered "Nuts". They fought for two days and held the Germans out until Pattons 3rd Army broke the siege. There are many many more examples. Heck was the war of 1812 over when the British captured Washington DC? No!
The point I'm trying to make here is that it is not fair to say the French did not fight back, but it is fair to say they gave up pretty easily once the capital fell. That is a big reason why so many speak of the French with disdain. But that is not deserved either. Most of the French today never surrendered to anyone.