Roman and Celtic sources describe the Druids as being the superintendent group in Gallic society, they filled the roles of priests, lawmen, writers and doctors. However most day-to-day governance took place on the tribal level, each tribe had a council of elder, and a king (later an elected magistrate).

The Romans roughly divided Gaul into the conquered Provincia, near the Mediterranean and Gallia Comata (Free Gaul) to the North, and Julius Caesar in his Di Bello Gallico further distinguishes 3 distinct groups; The Belgae, the Aquitani, and the Celts or Gauls.

The different tribes remained separate, although for the most part there were stable political relations between them, and even when they united it was due to extreme adversity and they remained separate factions fighting for a common cause.

Actually it was this Divide-and-conquer strategy that allowed Caesar to conquer as much of Gaul as he did, as he took advantage of their internal disputes and power struggles . And by the time Vercingetorix managed to assume chieftainship of the Arverni and formed alliances with the rest of the Gallic tribes it was too late. As for exactly how they were organized, they remained separate tribes, but Vercingetorix was given supreme command of the armies (which were comprised of the able-bodied adult males from the various tribes given the Gallic warrior culture, but not professional soldiers the way the Roman legions were).

Sources:

Di Bello Gallico by Gaius Julius Caesar

Celtic culture: A Historical Encyclopedia by John T. Koch

Life of Caesar by Plutarch

Life of Marius by Plutarch