The French
There exists a fairly detailed record of the French army from the 20th of April:
1375 "Lances"
613 Light cavalry
7489 Landsknechts
4000 French foot ("Aventuriers")
2500 Italian foot
18 'large' cannon
By the time of the battle this had been reduced by losses and detachments to about:
1100 "Lances" (3300 to 4400 combatants on paper)
500 Light cavalry
10000 foot soldiers
The artillery was reported by one source as 26-28 cannon ("from great Cannon to Falconets for the battlefield") while the Swiss claimed to have captured 25 cannon.
Each "lance" has at least 3 fighting men on paper, the man-at-arms and two archers. There is also the Coustillier who in the 15th Century was 2nd best equipped man in the lance but by the mid-16th century had been reduced to the role of armour bearer for the man-at-arms with no active role to fullfill in combat. The problem is that no one seems to know just what the role of the Coustillier was in the early Italian wars, was he still a fighting man or had he become a servant?
The archers are also a bit of a problem, they were orginially mounted infantry but evolved into cavalry during the Italian wars. As late as the battle of Ravenna a large part of them dismounted to fight with their longbows and the 1515 Ordonnance still has them armed with bows. The archers were well armoured with sallet, mail collar, breasplates and probably leg armour as well.
So far I have been unable to turn up any clues regarding the identity of the light cavalry. While the French had some Stradiots in service at the time they seem to have been in Northern France facing the English and Imperial armies rather than in Italy. So I'd lean more towards crossbow armed Argoulets rather than Stradiots.
The "Aventuriers" were armed with a mixture of crossbows, pikes and polearms (bills & halberds), the view found in most wargames army lists that the French foot was made up soley of crossbowmen apart from some Picard pikemen is not supported by the sources. There was a lot more troops armed for close combat present than the French get credit for.
It is recorded that the Landsknechts had 800 arquebusiers. If they used a organisation similar to that of 1515 almost 12% of the Landsknechts had firearms, a bit more than 16% "kurz wehr"( "short arms" i.e halberds and twohanded swords) and the remaining 72% pikes.
The Italians are a real problem, there seem to be few details available regarding their equipment in 1513. It is also unclear if any Italians were present at the battle, the sources mention only Landsknechts and French infantry.
Given the large number of landsknecht arquebusiers present is is likely that around 6500-7000 landsknechts took part in the battle supported by some 3000-3500 French Aventuriers.
The Swiss
The Swiss-Milanese troops was made up of 3 parts, the intial levy, the reinforcements and the Italians.
The first levy raised by the confederates was made up of 4000 made up contingents raised by the various cantons and cities. In addition it was joined by a large number of "free soldiers" joining as individual volunteers. All in all some 6000 Swiss troops marched into the Duchy of Milan with the 1st levy.
The 2nd levy was raised to reinforce the Swiss troops who were now under a fair amount of pressure in Milan. The cantons were supposed to raise a force of 8000 men but there is only evidence for some 4600 being assembled, to this was added perhaps some 1000 "free soldiers". With losses factored in the Swiss had at best 10000 men at Novara and 9000 may be closer to the mark.
The Swiss had some problems with their equipment as too many men turned up with halberds and/or unarmoured. A Swiss commander wrote home that the army was "overloaded with halberds" and had been forced to request the Duke to supply them with pikes.
The number of arquebusiers among the Swiss is also a problem as the Swiss could field a very varied number of shot depending on the year and circumstances. During the 1511 campaign 25% of the Swiss were armed with Arquebus but the year after there were only 79 arquebusiers among the 1500 men raised by Bern. At Novara there were enough arquebusiers to create a significant amount of smoke so I'd estimate about 900-1000 arquebusiers being present.
The Italians were few in number, there were supposedly some 1000-3000 Lombard infantry who remained in Novara while the small force of cavalry went out with the Swiss.
Just how many cavalry there were is a matter of debate. The French sources mention 500 cavalry which is obviously an exaggeration. The Swiss sources mentions some 100 mounted nobles while the Italian sources mention several hundred light cavalry. A problem is that most sources are chroniclers writing in later years rather than eyewitnesses.