Europe is a collection of very old localities and countries but most of these governments are young, younger than the United States. France is no exception. By the time WWII broke out, they were already on their third republic government. The first one was created in 1804 under Napoleon and today they are on their fifth one, established 1958. One might say that during all of those years France was always in the process of inventing and reinventing its government. Therefore, there have been periods when their politics did not serve them well.
The French people have proven themselves to be just as good as anyone. They are among the world leaders in just about everything; science, medicine, engineering, art, etc. And they have always maintained a good military with well trained soldiers. But when WWII broke out, it was their politicians who failed to step up.
Prior the the invasion of Poland, Édouard Daladier was the Prime Minister of France. He was not only a smart man but one of the first to accurately compare Hitler's ambitions to Napoleon. He knew what had to be done. He was a strong supporter in declaring war on Germany. But under pressure from other politicians and Neville Chamberlain, Britain's Prime Minister, he did very little.
On 7 September 1939, French troops invaded Germany in Saarland breaking through the Siegfried Line. They had the Germans in retreat. But on the 12th, the Anglo French Supreme War Council ordered the French forces to halt and retreat back to their Maginot Line. Britain and France had a golden opportunity to force a quick end to the war. But they chose to do nothing instead. Under this Anglo-French leadership, the following months of inactivity became known as the Phoney War.
After the war, Hitler's Chief of Staff Alfred Jodl said that, "If we did not collapse already in the year 1939 that was due only to the fact that during the Polish campaign, the approximately 110 French and British divisions in the west were held completely inactive against the 23 German divisions."
Daladier was forced to resign (21 March 1940) but not for his inactivity against Germany but for his doing nothing to support Finland when the Soviets invaded there. He was replaced by Paul Reynaud, another anti-Hitler man who many compared his views to Churchill's. But as it had been with Daladier, politics tied his hands too.
On 10 May 1940, Hitler's forces invaded the low countries (Luxembourg, Belgium and Netherlands) and then swung south into France. On 5 June, he launched a second prong attack as his troops bypassed the Maginot Line and drove deep into France. The French government surrendered on 25 June 1940.
The old French government was replaced by Hitler's Vichy France. This meant France and all her colonies were now a puppet government under German rule. This new government allowed for the French to administrate civilian affairs as long as nothing they did conflicted with German laws. This was good for Hitler otherwise his manpower and resources would be spread too thin in governing France and her colonies.
Here's where the history of WWII France gets harder to follow. There were those who went along with this new Vichy government and those who did not. While all her colonies were supposed to be under the Vichy government, some went along with it, some flat rejected it and others waited until events made it easier to reject. It is from these colonies that France was able to raise most of what became known as the Free French Forces, which eventually swelled over 1.3 million men.
Then there were those who could not leave German occupation. Many of those joined the French Resistance to help the war effort in whatever way they could. Without a doubt, the French Resistance played a big part in winning the war. No one knows how many were actively involved but after the war the French government recognized 220,000 men and women for their service.