On 14 June 1940, the open city of Paris was taken by the German army. There was no opposition. Le Havre in the north fell as to German control. The Maginot Line in the east was broken by the German 1^st Army under General Erwin von Witzleben near Saarbrucken. The French government had relocated to Bordeaux and appealed to the United States to enter the war. Prime Minister Winston Churchill had asked the French to hold on and not surrender.

In the United States, the fall of France was seen as a catastrophe but there was hesitation on what to do. The French premier Paul Reynaud asked President Roosevelt for aid in either a declaration of war or, if not possible, any help they could provide. Roosevelt was sympathetic but advisors such as Cordell Hull, the Secretary of State, argued any open support for the French would be seen as a declaration of war by the Germans. Public opinion was still in support of the U.S. staying out of the European war, and the Congress would not wholly support it either.

Parisians had been fleeing the approaching German troops. It has been estimated that over 2 million Parisians fled ahead of the German arrival in Paris. Parisians awoke that morning with messages blaring over loudspeakers that a curfew would begin at 8 pm that night. The Germans took quick control raising the German swastika on the Arc de Triomphe and the Eiffel Tower. The Gestapo quickly began to start rounding up those already on lists for arrest, interrogation, and execution or deportation to Germany. While the United States did not offer any formal support for France, it implemented a freeze on Italian and German assets in the country (meaning they had no access to funds in U.S. banks or to any property they owned).

By this time, the formal relationship between had already deteriorated. As a response to Kristallnacht in 1938, the U.S. ambassador had been withdrawn. Only a Charge d’Affairs*represented the U.S. from that point on. Germany withdrew its ambassador in response. This would remain unchanged until Germany formally declared war on 11 December 1941.

*A charge d’affairs is a diplomat who handles the ordinary duties of an ambassador when they are not present (whether temporary or permanent). Often this will occur when an ambassador has ended his tour and they are awaiting a new one to be posted. A person acting in this capacity has the same immunities that the ambassador does. In formal ceremonies, a charge d’affairs is treated with a lesser precedence than an ambassador.

Sources:

History.com
History.net
World War II Database