That makes a bit more sense, but those figures still sound too high to sustain for any period of time. So I'm trying to figure out how they'd be able to have enough supplies for that (for the relief force, you mentioned the fate of those within Alesia).
I don't want to dispute the figure, as I haven't studied this in particular, but being able to supply the (mid-point between the two extremes) 185,000 men of the relief force takes half a million tons worth of food. Daily. How are they transporting it all?
According to Peter Kehne, in Erdkamp,
A Companion to the Roman Army, and Kehne draws on Engels and Roth, the troops required about 1½ kg of food per day; their cavalry horses required 2½ kg of barley per day, and either time and pasturage or 7 kg of hay per day.
I would add that 120,000 troops is larger than any Roman field army. At Cannae, the Republic had slightly more than 80,000 troops; some armies at Pharsalus and Phillipi are comparable; Julian's army in Persia had slightly more than 60,000 and was divided into two forces.
But assuming - for the sake of these calculations - 108,000 infantry, 12,000 cavalry, and 40,000 military servants and camp followers - that's 240,000 kg of food, plus 114,000 kg of fodder per day. If Caesar hasn't already stripped the land bare, the relief force will do so after a few days without supplies. So they are going to need to bring the supplies from elsewhere in Gaul.
And the pack animals need to eat too. A horse - depending on size - can carry about 70 kg to 90 kg and will eat about 7½ kg to 9½ kg per day. So the pack animals will carry less than 10 days' supplies. A horse - again depending on size - can rarely pull more than 35 kg to 45 kg for any distance. So using wagons doesn't seem to solve the problem. So it all depends on the depot system, not exactly the Gallic forte.