The Free French army was in effect largely made out of Pied-Noirs and North/Central African natives; but units like the 2nd Free French Armored had predominantly white and metropolitan/expat Frenchmen.Of course, all Officers were White, expats from Metropolitan France or Pied-Noirs from North Africa (who were considered 'metropolitan' anyways in the 3rd Republic). In keeping with tradition, Foreign Legionnaires were led by French Officers as well.
Some units - like the aforementioned 2nd Armored, were attached to US Corps and fought largely under US command into the dash to the Westwall and beyond. In August, with the breakthrough in Normandy achieved, Operation Dragoon landed an American Army group that consisted of French Army "B" (Later 1st Free French Army) and the US 7th Army.
The First French army's largest land battle would be the reduction of the Colmar Pocket, and saw heavy fighting in heavy winter conditions.
So in short, they played a key role in the Liberation of their homeland and the pursuit of the defeated 5th Panzer and 7th German armies across France and into Germany. They would fight as an Army in the South in the Saarland, and as a smattering of individual divisions in the Center of the Allied line.