To give an example.
During the battle of Crecy modern historians place the number of french troops at 20,000-30,000 whereas contemporary sources places the number of troops at 72,000 to 100,000 .
Furthermore the number given by the contemporary sources seems believable if we consider that during the Gallic Wars Vercingetorix commanded a field army of around 30,000 - 45,000 with a large Calvary contingent when the regions population was a fraction of medieval Frances population.
With your Crécy example, we have a number of different ways to estimate the number of French forces present, although the administrative records that would allow us to know the exact number no longer exist. During the 1340 campaign in Flanders, a total of 22 500 men-at-arms, 2500 foot sergeants and 200 crossbowmen were either in the field or garrisoned in the area. Another 5500 men-at-arms, 12 200 infantry and 1800 crossbowmen were in the field or garrisoned in other areas of France. This puts a reasonable limit of 20-30 000 for French armies in the period.
With regards to Crécy itself, Edward III himself wrote that the French had 12 000 men-at-arms at the battle, of whom 4000 may have been professional crossbowmen (the confusion comes from some ambiguity of word usage during the period). To these need to be added the militias of the surrounding towns, abbeys and villages, though I'm not aware of any attempt to calculate the possible number of them. It's unlikely to have exceeded much more than 10 000 - towns typically only had to provide infantry to serve within half a day or a day of their town, and at least 2000 militia missed the battle. In addition, the English had killed or defeated various militias on their march north.
On the English side of things, we have excellent documentary evidence for their army sizes dating back to the 12th century - very rarely do they exceed 10 000 men in any individual army - and these numbers are usually considerably smaller than those supplied by chroniclers at the time. Those authors who were in a position to know the true size of armies (such as chancellors) also record quite small armies that contrast with the much inflated numbers from contemporary chroniclers. Some administrative records also exist from Italian towns and towns of the Low Countries that routinely provide quite good information on army sizes after the 13th century (although some examples in the 13th century exist).
I don't know enough to properly discuss the disparity in army sizes between Antiquity and the Middle Ages. I am, however, quite sceptical of numbers from Antiquity in general.
Further Reading
War Cruel and Sharp, by Clifford Rogers
The Battle of Crécy, 1346, ed. Andrew Ayton and Sir Philip Preston
The Art of Warfare in Western Europe in the Middle Ages, by J.F. Verbruggen
War in the Middle Ages, by Philippe Contamine
Armies and Warfare in the Middle Ages, by Michael Prestwich