From what I've read on French websites, Soldat is really the basic rank whilst Fusilier (or Grenadier, Carabinier, Voltigeur, Chasseur, depends on the type of soldier) is like a specialisation. Soldat de Première classe isn't really a rank, it's just a distinction given to soldiers that did something special or very brave in a battle so it's kinda useless to say Soldat de Deuxième classe in fact.