This month, Amable Sablon du Corail, the director of Middle-Ages and Ancien Régime departments at the French National Archives and author of 1515, Marignan wrote an article in the paper 'L'Histoire nb 68. The edition is dedicated to King Francis I of France and there is a very interesting page about the battle of Marignano in 1515 and the composition of the army.

So keep in mind that the numbers below are about the French army in the early reign of Francis I ( ruled 1515-1547 ) and not about the whole Renaissance.

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Francis, as his predecessors had done since Louis XI managed to buy the quietness of England ( with some 5% of France's annual revenue ) allowing him to fully commit his army to the French Italian ambitions. In July 1515 when Francis gathered his forces and headed toward Italy, the army was composed of some 40,000 men ( maybe 45,000 but not more ) , almost twice as much as the other big powers in Europe. This was mostly due to the huge demographic explosion France knew, meaning it was the most populated country in Europe at the time.

Quite a novelty, the army was mostly composed of infantry. However, cavalry was still a big thing and Francis had 2,500 lances and 5,000 archers on horses ( direct quote from Sablon du Corail ). To that, the army had 56 culverins of ordinary or extraordinary calibers.

What is interesting to see in Renaissance armies ( at least France's ) is their reliability on mercenaries. Still in Francis' 1515 army, most of the infantry was composed of German troops, around 23,000 Landsknechts formed the heart of the army. The Renaissance saw the advance of firearms ( artillery but individuals as well ) however the French army relied heavily on its 8,000 thousands crossbowmen from Gascony. This enormous army was extremely expansive; a monthly cost of around 300,000 livres tournois of the time ( Maybe someone could try to find an equivalent ? But the author only says this was what the Duchy of Milan made every year at the time ). Armies were far from being fully professionals at the time and countries relied a lot on buying the services of mercenaries ( German or Swiss for examples ).

The army was also followed by many glory seeker adventurers, unpaid but attracted by the spoils of war and the chance to make a name. These men were, still according to Sablon du Corail several thousands at the battle of Marignano but a more precise number is close to impossible to find.

In the same paper, a small article written by Emilie Dosquet, PhD student in military history at Paris-Sorbonne writes that the armies of time ( especially France, she does not say anything about other powers so I only speak for France ) knew a huge increase in numbers. Twenty years before Francis I, King Charles VIII and his vassals could gather around 18,000 men ( compared to the 40,000 of Francis ). By 1515, the army was composed of three infantrymen for one horseman when 20 years ago the army was composed of two third cavalry. At the time of Marignano, France had the most powerful and modern artillery in Europe thanks to technological advances ( lighter cannons,...Etc ).

However, if France had the number it also lacked the use of lighter guns ( individual ones ) which were beginning to spread in other powers like in Italy and Spain. It still relied very much on the cavalry and the spirit of knighthood. A mix of Middle-Ages and Renaissance military doctrines that made Francis pay a heavy price in 1522 at Bicocca where the Swiss mercenaries launched a beautiful but foolish assault on fortifications and then in 1525 at Pavia where the army was crushed and half the aristocracy killed or captured.

Remember this is specific to France in the early 16th century. At Marignano, France left around 5,000 dead soldiers ( French or in French service ) and ten years later at Pavia the casualties on the French side were close to around 12,000 dead, incapacitated or captured soldiers ( including the king and many captains ). It changed drastically the composition of army.