Yes, Vichy France had Army of the Armistice (or Armée de l'Armistice). Under direction of the German army, it was meant to defend from the Allies.

As far as the Free French Army goes keep in mind there were other French servicemen too. Many escaped to England, indeed French pilots flew in the RAF in the Battle Of Britain. The British, fearing the French Navy ships would be captured by the Axis destroyed three ships at Mers El Kebir after the French refused to accept an ultimatum to concede the ships to the allies. Some French Naval vessels went to out of the way places and just sat out the war, others saw action in a number of battles, both against Vichy French Forces (mostly in North Africa) and the Axis, indeed some ships took part in D-Day as well as the Battle of the Atlantic.

The North African battles against the Vichy French were important, as by re-gaining the French colonies there de Gaulle boosted the number in his army. By the end of the war the Free French Army was over half a million men strong.

The Free French Army fought in Syria and North Africa - including the battle of El Alamein, where the Allies defeated the Axis and is widely seen as a turning point in the war as well as Operation Torch.