Why shouldn't they be? Over a million Free French soldiers participated in the war against the Axis powers. The Vichy government did not simply 'still control the colonies', only some, and even then those could end up in Free French hands, see Madagascar. The government in exile was recognized by other powers and continued the fight. Even if we disregard the beginning of the war and the Battle of France, the French fought in Africa for example at the second battle of El Alamein, in Italy and in France, including the invasion of Normandy and the liberation of Paris.

All the points are true. The answer is simply because while France's contribution to victory was indeed small, the country could play an important part in an post war Europe.

Churchill proposed in the Yalta conference that the french zone in Berlin be created using the area allocated to the US and Britain. He stated to Stalin that France could be important after the war. Maybe Churchill wanted an old power to remain active in the world stage to counter the growing influence of Russia and the United States.

The Allies needed French cooperation in North Africa to defeat the germans. It all began there. That political alliance helped the allies be viewed as liberators when the Nomandy landings happened. The Free French were received as saviours of France's Honor.

Their contribution was small but significant in certain battles. French colonial troops were decisive in the mountain warfare in Italy. The French Corps helped break the Gustav Line in 1944. The french fought well into southern France until internal conflicts between communists, Free French and prior Vichy-Government members limited effective employment of France's army around Strasbourg.

Source: Rick Atkinson's series, An Army at Dawn, The Day of Battle and Guns at Last Light.