Whao, that is a short question, but the answer is quiet long.

These figures are not from my own research, and I delete some comments which could have been seen as offensive… These are my comments
FFI (Forces Françaises de l'Intérieur - French Forces of the Interior) - about 200,000 men and women
FFL (Forces Françaises Libres - Free French Forces): about 500 000 men (in majority), 560 000 men on the 1st of September 1944 and 1 million men at the end 1944.

The FFL denomination for "Forces Françaises Libres" is in fact only used for the French volunteers until the 31st July 1943. After that, the term "Armée Française" (French Army) is officially used. In fact, since the 14th July 1942, the general De Gaulle employed the denomination "France Combattante" (Fighting France) for all the French troops participating to the liberation effort, including the resistance which gave rise to the FFI.
- in the army
- in the navy (10 000 men in the Royal navy and on FFL vessels)
- in French air force but also in allied air forces (about 3 500 men in the RAF and in the soviet air force) In the RAF there were about 150 French aces (= at least 5 confirmed kills) : Pierre Clostermann (33 kills), Marcel Albert (23 kills), Jean Demozay (21 kills) etc. In the Soviet Air Force there was the GC.3 "Normandie Niémen" Squadron (273 confirmed kills).

The French air force in 1943-1945 was composed of :
In UK :
- 4 fighter groups (Alsace -Sqn 341-, Ile-de-France -Sqn 340-, Cigognes -Sqn 329- and Berry -Sqn 345-)
- 3 bomber groups (Lorraine, Tunisie and Guyenne)
- 2 transport groups (Artois and Picardie)
In USSR :
- 1 fighter group (Normandie-Niemen -GC.3-)
Under US command in North Africa, Sicily, Corsica, France etc.
- 9 fighter groups (Nice -Sqn 326-, Corse -Sqn 327-, Provence -Sqn 328-, Roussillon, Champagne, Navarre, Lafayette, Dauphiné and Ardennes)
- 6 bomber groups (Bretagne, Maroc, Gascogne, Bourgogne, Sénégal and Franche-Comté)
- 1 reconnaissance group (Belfort)
- 1 transport group (Anjou)

French forces already fought on the allied side in 1940, and the battle of France is generally known only through the prism of caricatures, myths and generalization ... also often ignored the Free French involvements in 1941-1943.
On 18th June, 1940, General Charles De Gaulle broadcasted an appeal on BBC radio for French men and women to join him and the British in the fight against Nazi Germany. But, by the end of July 1940 only 7,000 people had volunteered to join the Free French forces. The attacks on the French Navy at Mers-El-Kebir and Dakar caused bitterness in France and did not encourage former members of the French Army to escape to Britain. Nor the political will of Petain...

Many combats in North Africa from 1941 to 1943: Leclerc's column (ancestor of the 2e DB) took the Koufra oasis in Lybia to the Italians in 1941 and all the Fezzan area (SW Lybia) between March 1942 and January 1943. Leclerc’s force quickly crushed the Italian defence in southern Libya and marched 1500 miles north reaching Tripoli on January 23, 1943 just as the British arrived from Egypt. Leclerc placed himself under the command of Field Marshal Montgomery and his corps played a major role in the advance of the 8th Army on Tunisia. He was promoted to General de Division on May 5, 1943 and ordered to Morocco to form the 2e DB (2nd Armoured Division). Free French soldiers participated in allied campaigns in Egypt, Lybia and Tunisia. General Koenig and its 1st DFL did particularly well against Afrika Korps in Bir Hakeim in June 1942. Free French forces also fought Italian troops in Eritrea and Ethiopia and faced French troops loyal to Vichy France in Syria and Lebanon.

About 120,000 French soldiers fought in Italy in 1943/1944 in the French CEFI (Corps Expéditionnaire Français en Italie) under the command of general Juin. The CEFI allowed to take Monte Cassino by piercing more south in the Monte Majo, a much more mountainous area but general Juin's Goumiers and their mule packs did it and broke the front where the Germans didn't expected them. They also opened the doors of Rome to the allied forces on 4th June 1944 after a series of battles: Garigliano, Pico ... In Italy they lost 7 000 KIA, 30 000 WIA and 42 000 MIA.
In mid 1944, the Free French forces numbered about 500 000 men. The French CEFI is used as basis to build the French 1st army under the command of general De Lattre De Tassigny. This army landed in Provence during Anvil/Dragoon. The French 1st Army liberated both of the large French Mediterranean harbours Toulon and Marseille. The French 1st Army participated in pushing the Germans out of France (liberation of Toulon, Marseille, Lyon, Villefranche and Autun etc.) and back to the Rhine and the Danube. This operation is generally not well known, probably because 3 US divisions were involved in comparison to the 7-8 French divisions. The cities of Toulon and Marseille as it is the case for the Elba and Corsica islands were liberated by only French troops.
Toulon and Marseille fell to the allies on 28 August. They were soon handling more supplies than all the Normandy ports combined, and proved a logistical life-saver for the continued allied advance across France. Patch's 7th army linked up with Patton's 3rd army near Dijon on 11 September. The French 1st and US 7th armies were organized into the 6th army group under US general Devers (15 September), and served on the southern flank of the allied armies, advancing through Alsace-Lorraine into Germany and Austria by VE-day.

On the allied side during Anvil/Dragoon :
The Naval Western Task Force (Admiral Hewitt, USN) with 2120 ships including 359 combats and escort ships, 600 large transport ships and smaller vessels.
There were indeed only 34 French combats and escort ships including :
1x battleship : "Lorraine"
5x cruisers : "Duguay-Trouin", "Emile Bertin", "Fantasque", "Terrible" and "Malin"
5x torpedo boats
The MAAF (Mediterranean Allied Air Force) (General Ira Eaker, USAF) was composed of 19000 aircrafts.
The French air force participated only with :
6x fighter-bomber groups on P-47
4x bomber groups on B-26
1x reconnaissance group on P-38

The ground forces were composed of 3 US divisions (36th, 45th and 3rd infantry divisions + several small rangers and airborne units) and 7 divisions of the French 1st Army + not endivisionned units (Bataillon d'Afrique (commandos), Bataillon de Choc (commandos) etc.)

The 1st French Army was organized in 2 corps :
- 1st corps under the command of general Béthouart
- 2nd corps under the command of general De Goislard de Monsabert and they are composed of :
- 1e Division Française Libre (motorized infantry division)
- 2e division d'infanterie marocaine (infantry division)
- 3e division d'infanterie algérienne (infantry division)
- 4e division marocaine de montagne (mountain infantry division)
- 9e division d'infanterie coloniale (infantry division)
- 1e division blindée (armoured division)
- 5e division blindée (armoured division)
+ independant elements :
- Bataillon d'Afrique (commandos)
- Bataillon de Choc (commandos)
- Bataillon de France (commandos)
- Four GTM (groupements de tabors marocains) (infantry)
- 9e Régiment de Zouaves (infantry)
- 1e Régiment de Tirailleurs Algériens (infantry)
- Two Chasseurs d'Afrique regiments (RCA) (armored regiments)
- Three Spahis regiments (recon armored regiments with armored cars and Stuarts)
- One Régiment Colonial de Chasseurs de Chars (armored regiment with tank destroyers)
- 2e Régiment de Dragons (armored regiment)
- 64e, 65e and 66e RAA (Régiment d'Artillerie d'Afrique = African artillery regiment)
- Régiment d'artillerie coloniale d'Afrique occidentale française
- Régiment d'artillerie coloniale du Levant
- Four engineer regiments and one bridging battalion

----> During late war several other divisions joined this Army :
- 27e division alpine (mountain infantry division) who played a role in the Alps in 1944 (formed on the basis of the former 1e division alpine).
- 3e division blindée (armoured division) (created sooner but disbanded in September 1944 and recreated in 1945)
- 1e division d'infanterie
- 10e division d'infanterie
- 14e division d'infanterie
- 19e division d'infanterie
- 23e division d'infanterie
- 25e division d'infanterie
- 36e division d'infanterie
- 1e DCEO (Division Coloniale d'Extrême Orient)
- 2e DCEO (Division Coloniale d'Extrême Orient)

All the late infantry divisions for the most part comprised former FFI ("French Forces of the Interior") groups. These divisions served mostly in security, garrison and occupation roles. Except the alpine division which included many former "chasseurs alpins" and fought in the Alps in 1944/1945, the battle efficiency of new infantry divisions was rather low, the freshly enlisted men were not trained to the modern combined arms warfare and had to learn.
The French armoured divisions were organized for combat like the US AD, in "combat commands" called GT (groupements tactiques) in French. The 2e DB was assigned to Patton’s American 3rd Army and landed in Normandy on July 23, 1944. The unit saw its first action in the effort to close the Falaise pocket and liberated Argentan on August 12th. The Free French 2e DB led the drive towards Alençon and Paris. The losses during the battle of Paris (with one US division) where followings :
Allied troops :
130 KIA, 319 WIA, 21 MIA
48 tanks, 4 guns
German troops :
3 200 KIA, 12 600 POW
74 tanks, 64 guns, 350 various vehicles

The 2e DB made junction with the 1st French Army on 12th September 1944. French SAS were involved for D-Day already on the 5 June and played an important role. The 177 French commandos-marines participated also long before the Normandy landing like the French SAS (see notes). During D-day these French commandos (troops n°1 and n°8 of the 4th Commando) landed at Sword Beach in front of Ouistreham and the strongpoint "Riva Bella". The French Commandos-Marines were used later in other operations, especially in the Netherlands. At Walcheren for example, the first assault was led by the troops of the 4 Cdo with the French commandos-marines. They landed in Vlissingen (uncle beach). 5 hours later the Royal Marines 41, 47, 48, a Dutch troop and a Norwegian troop landed at Westkapelle. After that came the battles in North East of France, especially in Alsace. Liberation of the Belfort area, and then in Alsace : Colmar pocket, liberation of Strasbourg and all the battles during operation Nordwind ... and then southern Germany and Austria. In the Vosges/Alsace battles (where about 25% of the allied forces were French) during 1944, French ground forces were the first reaching the Rhine (not crossing it) on 19th November 1944 and then they entered south Germany and Austria : Kehl, Karlsruhe, Neckar, Pforzheim, Tübingen, Stuttgart, Rottweil, Uberlingen, Sigmaringen, Bregenz, Bludenz ... They were also the first reaching and taking Berchtesgaden and the "Adler's nest" with the US 3rd ID. A battalion from the US 3rd ID was followed by the French 2nd Armored Division. The French were the first Allied troops into the Eagle's Nest at the top of Kehlstein Mountain, followed by C/506th, and members of the 321st GFA battalion.. On 8th May 1945 the general de Lattre de Tassigny represented France during the capitulation of Germany.

During WW2 France lost about 253,000 KIA (92,000 alone during the 45 days of the 1940 campaign) and 390,000 civilians killed and of course numerous mutilated people.