The Germans invaded Holland and Belgium on May 10, 1940. True to plan, as the Germans expected, the Allies marched into Belgium for the main force engagement. Some Belgians tried to stop both the Allies entering from the South and the Germans entering from the Northeast. Little attention was paid to communication and intelligence between the three Allied Armies.
Thus, what could have been a powerful coordinated Allied Army became three separate armies speaking several different languages. The Allies never practiced or trained together, and they often neglected to even tell their own countrymen where they were during the battle. France and Britain were completely unprepared for German General Heinz Guderian's tanks to burst out of the Ardennes, and the Allies failed to stop them at Sedan. By May 28, when Belgium surrendered, the situation was critical and the BEF was evacuated from Dunkerque by June 4. Weygand replaced Gamelin as senior commander and put a stop to Gamelin's plan to reroute the first line French forces to march against Guderian. That sealed France's fate and on June 22nd, the new Vichy government under Philip Petaín sued for peace.
It's hard to imagine today, with so much prejudice against the French Army's abilities, but in 1940 the Fall of France shocked the world, and more so the French people. Some 200,000 french soldiers were dead, and while France's colonies held significant forces, Vichy was unwilling to commit them to the British cause, so Britain attacked key installations in North Africa to prevent the French Navy from falling into the hands of the Germans.
Vichy remained in control of the lower half of France, while the Germans occupied Paris. Hitler came to Paris to see the Eiffel Tower and comtemplate his success at Napoleon's tomb. The Gestapo came to France to begin a terrible occupation that would eventually see hundreds of thousands of French citizens forced into slave labor.
At first, the communists stayed out of resistance activity at the behest of Stalin, but with the German invasion of the Soviet Union in June 1941, Communists took the lead in resistance activity. The Gestapo drove Former French soldiers, communists, and socialists, as well as disillusioned Vichy officials, into remote areas of France to hide, where they organized. By 1942 eight major resistance groups baed on political affiliation and geography were active, rescuing Allied pilots, striking German transportation, and distributing illegal propaganda. At DeGaulle's urging, Jean Moulin was dropped into France by the Special Operation Executive (SOE) and he unified the resistance into a single command. While the resistance has become romanticized, they were never more than partisians, and were unable to fight the Germans in the two pitched battles known to take place. Jean Moulin was arrested by the Gestapo and executed, but the resistance he unified was able to provide substantial intelligence to the Allies when they invaded in 1944.
At the time of the Normandy invasion, the Germans were drawing increasingly on forced French labor. French citizens had to make a choice: sign up for a ration card to get food, but a ration card meant you were liable to be drafted and sent to work in German factories. Hundreds of thousands of French were shipped to the Reich, were they often had little to eat and worked for days without a break on munitions.
The Allies were greeted as liberators throughout France, but especially DeGaulle's Free French divisions. A second landing was made in Southern France in August 1944. By December 1944 most of France, except for the channel ports holding out on Hitler's orders, was in Allied hands.
DeGaulle and the resistance leaders were heroes, but the Vichy government was considered traitors. Petaín was sentenced to life imprisonment and died there in 1951.
France was a founding member of the United Nations, and is one of the five permanent members of the Security Council.