I think this is an interesting question, certainly it is to me, and it's a shame you haven't gotten a good answer yet. So I decided to have a look into it for you in the meantime. I should emphasise that I don't know much about this period and so, until I read a few things on the matter, I knew next to nothing of this issue.

I found a very surprising answer to your question in a journal article. After pointing out the demographic size of Charlemagne's empire was around 20 million people (351-2), the author claims that "In light of the size of the population of Charlemagne's empire, it should not be surprising that those who study Carolingian military demography now see the emperor as being able to put into the field for offensive military operations, intended for the conquest of enemy territory, several armies in any given year, which when taken in the aggregate could reach a total in the neighbourhood of 100,000 effectives" (Bachrach 352-3).

As a student of the Roman military, and understanding as I do the incredible logistical organisation and resources that made the size and reach of Rome's armies so formidable, I find it incredible that a medieval empire, even one was large as Charlemagne's, could field such forces, even if only for a single campaign! Since I personally find this a fascinating claim, I went through Bachrach's footnotes for this number. Bachrach claims that, despite what I thought personally, that the Carolingians could raise very large armies is much the majority position for medieval military specialists. Bachrach cites a single specialist in the field who resists the general rule that the Carolingians could field huge forces, one Timothy Reuter. Reuter apparently sees individual Carolingian armies that could campaign for any extended period as not much bigger than 2000-3000. However, his selective use/misuse of casualty lists to support such low figures is criticised by Bachrach, and the latter's case seems sound. Indeed, going from casualty lists, such a contemporary list giving a number of "5000" for a defeated Viking army in 880 AD, it seems such sources could easily be used to support a view counter to Reuter's.

Charlemagne's status as by far the greatest European power of his time, and wide range of his campaigns (stretching into the Pyrenees, Saxony, Bavaria and Italy: see Bennett 89-91), do make it seem as if large and yet sustainable fighting forces that could be summoned readily would be necessary for such campaigns. With the fall of the Roman government in Europe, and the settlement of most barbarian groups in some place or another, warfare in Europe became a local rather than a state affair, with the corresponding reduction in available resources. According to the Cambridge History of Warfare, it is Charles Martel, Pepin (d. 768) and of course Charlemagne were the first after the fall of Rome to re-develop a centrally controlled military system (Parker 68). The Cambridge History gives details of how this recruiting system works (though the authorities came up with various formulae), which may give us some insight into how such incredible armies could be used for organised offensive campaigns in Europe even after the collapse of the Roman logistical system:

The selection of levies from various territories formed the basis of the Carolingian Army. Apparently rich men with twelve estates or more were required to muster with horse and armour when called. Men with five estates were also liable to being mustered, but with less equipment. Those living close to the field of operations could be called up with three or four manors, and landowners with as little as half an estate were formed into "partnerships" with a total wealth of five estates, and were required to provide and equip a soldier for the levy. Like the Merovingians, the Carolingians required all free men to take oaths of fidelity to the king and be registed on the rolls of their county. This identified those eligible to serve in both local defence forces and the levy, and gave central control over the "many thousands of highly professionalised fighting men who served in the personal armed followings of the lay and secular magnates" (Cambridge History 70).

According to the Cambridge History, Charlemagne controlled an even larger area than the Byzantines, who had lost the battle of Yarmouk and with it nearly half their territory. "Charlemagne...could muster for simultaneous major campaigns perhaps 150,000 men, of whom at least 35,000 were heavily armed mounted troops. Indivdual armies of 35,000 to 40,000, though hardly common, were not unknown" (70). Importantly, it is mentioned that "Charlemagne's grandons ...among whom the empire was divided in 843..tended to deploy smaller armies numbering from 8-10,000 in comparatively restricted theatres of operation."

For purposes of comparison in this period, the Byzantines, who had consolidated their position by the mid-800s, could field a regular army of around 120,000 troops (Cambridge History 75), with a field army of 25,000, supported by a population of eight million. With the breakup of the Carolingian empire, such huge armies disappeared in Europe again: King Harold levied 8000 troops at Hastings, and French leaders in the 10th and 11th centuries fielded relatively large armies of under 10,000 (76). William the Conquerer invaded England with 14,000 troops, including mercenaries. However, the army raised for the First Crusade under the aegis of the Church and led by a Bishop, was about 60,000 men. This was huge for an individual army, "double the order of magnitude of those raised by Charlemagne, and its logistic range was considerably greater..." (77). Of course, even in its debilitated state the Late Roman Empire had a standing army of something like half a million troops, though its field armies were still about the same size as Charlemagne's.

So there you have it. Charlemagne's armies could easily total 30,000+ men, and he could field several at a time if necessary, for a total of 100,000+ troops. The development of this incredible military capacity began with Charles Martel and peaked under Charlemagne. The numbers I have given were for the Carolingian empire, which existed from AD 800, and Charlemagne died in 814. At the start of Charlemagne's reign, when he had not conquered all the territory that he would later come to rule, his army would have been smaller. But I don't know how much smaller.

Thank you for asking this question so I had the opportunity to learn so much on the topic!

Sources:

Bachrach, Bernard. "Charlemagne and the Carolingian general staff", The Journal of Military History, 2002, 313-57.

The Cambridge History of Warfare, ed. Geoffrey Parker, 2005.

Bennett, Judith. Medieval Europe, A Short History: Eleventh Edition, 2011.

Follow up: how well-trained and equipped was his army compared to others of the time?