I have a few sources on my book shelf, some of which I believe more than others.
The Italian Wars by Mallet and Shaw:
Pg 30 States the French had 10,000-11,000 men and Gonzaga had 20,000 men – about a quarter Milanese, the rest Venetian and some Venetian Militia.
The French Military Campaigns 1214 to 1524 by Hardy de Parini and translated by G.F Nafziger.
This document gives far more details of the French forces as it is written from a French point of view. I also believe it overstates the Venetian forces perhaps to make the French victory seem even better.
For the French it states that the following forces marched down to Naples: 3,600 lances (21,600 horse – 6 horses per lance), 10,000 archers or Breton crossbow, 8,000 Gascon Arquebusiers, 8,000 Swiss of German Pike, 140 large guns, 200 light canon and 100 Arquebusier a croc.
Later it states that 500 Gendarmes, 2,5000 Swiss and few French were left to guard Naples and that 1,000 French Lances, 300 Italian Lances, 3,000 Swiss, 2,000 Bretons or Gascons and 42 cannon including 14 large guns left for France.
The natural question here is what happened to the rest of the troops. They certainly did not die on a battlefield as the trip was mostly a sight seeing trip. So you can either believe or not believe the units under the King for the trip back to France.
Later it details some of the French Forces:
The Avant Garde under Marshal de Gie contained 300 Men at Arms, 3,000 Swiss and 300 Archers of the Guard that the King had dismount. With these Archers were a few horse crossbow men of the 200 of the Guard and the rest of the army's infantry, that is to say the German Landsknechts commanded by Antoine de Bessy.
The Rear Guard under Count Odet de Foix contained 80 Lances of the Duke of Orleans, 40 Lances of Sire de la Tremoille, 100 Scottish Archers, 20 Ecus and others of the Kings household and pensioners.
No details are given of the Battaille under the command of the King.
On the Venetian side:
Attacking de Gie was the Count de Caiazzo with 400 Men at Arms, following them were a large force of infantry, behind them came another 200 Men at Arms.
Under the Marquis of Mantua were 600 Men at Arms, who were accompanied by by horse crossbow men, stradiots and infantry.
The book does mention 5,000 stradiots, but I just don't believe that the number came close to this amount.
The Art of War in the 16th Century by Charles Oman has some further information:
On pg 107/108 It list the Venetians/Milanese as having 2,400 Men at Arms, 2000 light Cavalry (mostly horsed crossbow men but including 600 stradiots) and 10,000 infantry (mostly crossbow but its some German pikes). It mentions that the German pikes were little better than camp followers.
These were deployed as follows:
Extreme right: Light horse (half Stradiots under Pietro Duodo and half horsed cross bow under Alessio Beccacuto.
Next on the right as the Count of Caiazzo with 600 Milanese men at Arms and 3,000 infantry (Milanese and German?).
Next as the Marquis with 500 men at Arms, most of his following but including some contingents of smaller allies. 500 horsed crossbow and 4000 infantry,
The left led by Fortebraccio de Montone had 500 Venetian Mercenary horse.
On the right behind Caiazzo there was another body of Milanese horse under Bentivoglio and Palavicino.
In the centre rear was troops from the Marches and Papal States under the Duke of Urbino.
In the rear on the left under Gambara de Brescia were a body of Venetian horse.
The French had:
The vanguard under de Gie had 350 Men at Arms, 300 Cross bow and 200 Mounted crossbow of the royal guard who fought on foot and 3000 Swiss pike.
The main battle and the rear guard each had about 300 men at arms and 2500 crossbow men a piece.
Oman gives a lot of details and it is tempting to take these on face value. However, a lot of research that I carried out on the battle of Novara, on which Oman was also very detailed, showed very severe differences with Oman – almost to the point where I could not believe anything that Oman said about the battle. I am therefore always skeptical about believing Oman.
Piecing all this information together I would estimate that the French had about 10,000 – 11,000 men. The Venetian totals are a little bit more difficult to estimate. A case could be made as many as 20,000 to 25,000, but 15,000 -20,000 seems more realistic to me.