Your very simple question has quite a long and comolicated 2 part answer. First lets cover what france actually did during ww2 then how it was tought in the US and France.

When talking about the French contributions it is important to remember there are two phases to the french peoples actions during ww2.

The first phase would be during what in my and many modern historians opinion is unjustly called the "phoney war". During this period between the start of hostilities in the 3rd of September 1939 and the 10th of May 1940, the French acted a unified goverment in the Third French Republic. The third french republic during this period was the second largest allied power just behind the British empire. The french cooperated with the british in the preparation to rebuff a German invasion into the low countries, opening an anglo-french front in the Balkan in the hope of saving Greece, sending aid to the Finnish during the winter War, assisting the British in their attempts to defend Norway from German invasion, and even launching a short-lived offensive into Germany in the form of the "saar offensive". During this period french forces mainly acted as a secondary force rarely acting independently of the British Empire. Their military was hampered by their political defensive doctrine in land, sea, and air. The french forces were never given the logistical support by their government for them to go on any meaningful offensives. The french politicians were fearful of a repeat of ww1 and felt their country would be better served shoring up defences along the Maginot line in preparation for a German invasion.

The french alone are not to blame for this indecision as the British also found themselves outmanuvered at every turn by the Germans both politically and militarily. This period culminated in the battle of france where the much anticipated German invasion came and unexpectedly slipped in during the Ardennes forrest. The ingenuity of German strategy added to by brilliant German officers on the ground and a huge serving of luck compleately shattered allied battleplans. The Germans had managed to cut off the best professional troops in the french army along with the british expeditionary corps. By doing this they had also out flanked the Maginot line, leaving only inexperienced and poorly equipped conscripts between them and Paris. Eventually the French surrendered but not before transferring their administration to the southern french city of Vichy. (Please understand many of these events I've glossed over in the hopes of giving you the context needed to answer your question)

Now begins phase two of the french war effort where the french forces can be roughly divided into 3 sub-groups. The chief among these was Vichy France which governed and administered the unoccupied parts of Southern France along with its substantial colonial holdings. Vichy france maintained the most equipment from the third french republic including the majority of the pre war french navy, airforce, and ground forces. The Vichy french would find itself in a very awkward position as it was now officially an axis ally while at the same time promising the British that its forces would not engage them in any significant way. The main worry by the british was the french navy held by Vichy france was quite substantial, if the germans could rest control of those ships the German navy would have more than doubled in size and capability. The Vichy french found themselves at odds with allied powers in Syria and North Africa aswell with limited hostilities taking place there. The vichy french would continue to fight the allies in limited capabilities until 1942 when the German and Italian militaries invaded/occupied southern France thus ending their quasi independence.

The Second sub group would be the Free French Forces under Charles de Gaul. The free french forces were composed out of those french men that had managed to escape at Dunkirk and those french ships, pilots, or soldiers which independently escaped to Britain. They formed a goverment in exile while allying themselves with the British Empire. The Free French were imediately after the battle of france much weaker than the Vichy french by all metrics. The Free French would never again be a leading allied power it was semented as a small power for the rest of the war. The Free French fought various campaings in the Sub-Saharan french colonies in africa against the Vichy french. There they suffered defeats against the Vichy french in west africa but made substantial headway in the central african colonies. There they would remain as a thorwn to axis strategic goals until the dissolution of Vichy France in 1942. At which point the Free french were able (with the substantial help of american and british forces) to liberate the entirety of their african holdings. The Free french were then able to assist the major allied powers more directly in the final north african campaigns against the allies as they were bolstered by colonial recruits and allied lend lease. The free french were very helpful to the allied wareffort during the north african campaigns mainly in securing allied flanks and providing a logistical base for the allied to use. The free french would then see their fiercest fighting yet during the Italian campaign where as many 150,000 Free French troops participated they were an integral part of the allied front lines during the campaign. The free french forces also contributed greatly to the formation and organization of the third french sub group of the war, the french resistance. (Information continues to be glossed over but please note that the British was the main allied fighting force during this period. Later during ww2 the americans were the ones that were able to break Vichy french forces in north africa. The free french were a vital but auxilary force)

As early as july 1940 there are axis reports of french partisans engaging axis forces in the forrest and mountains of france. These attacks carried harsh reprisals by the German forces, they were also quite disorganized. The early resistance was not uniffied and was compromised mostly of citizens militia independently resisting the German occupation. If the situation continued this way the french resistance would be crushed by the axis in short order. The Free french and British sent over supplies, advisors, soldiers, and spies. All in hopes of training, equiping and organizing the french resistance into not only a viable combat force but a vital inteligence arm to the allies. The free french contributions to the organizing of the french resistance was vital for their assistance during the liberation of France. (Again glossing over a lot here. While the free french were instrumental to the organization of the French resistance, it was the british that provided the supplies and command infrastructure necessary for its effective organization. At best the free french and British were equal partners in the formation of an effective French resistance)

During the D-day operations the French resistance was vital in its success. Many a supply line or troop convoy was disrupted by the resistance during the invasion adding greatly to the operational chaos. Three months after D-day, operation Dragoon was launched in southern france. The operation was a joint allied operation with many smaller allied forces assisting but the main invasion force was compossed of American army and free french forces. They found themselves oppossed by German and Vichy french forces. Yet again there were french men on both sides of the front lines. Like its larger brother d-day operation dragoon was considered a sucess also in no small part to the french resistance which was by this point im full revolt against axis forces. In the weeks of hard fighting ahead the French resistance intensified and joined up with the Free French forces as allied forces advanced through france. Many adhoc units in the free french forces from french resistance fighters in these weeks. It eventually culmimated in the liberation of Paris. Where the french resistance rose up in direct opposition to axis and Vichy french forces. As the american 3rd army was poised to liberate it. This was unacceptable to Charles de Gaul and he petitioned for Free french forces to be the first to enter the Capitol city. So it was that Parisians in full revolt were reinforced by the Free French forces, this was a moral and political godsend to the French. (The war was by no means over at this point nor was all of framce yet liberated but thats really what you need to know for part 2 of the answer)