Malplaquet is a very significant battle of the Wars of Spanish Succession and yet, it is really difficult to get any reliable information on troop strength. Wiki has strengths at about 86,000 and 100 guns for the Alliance to 75,000 and 80 guns for the French. If you dig deep enough and find some alternative pages, you can get a squadron and battalion breakdown for each side. The French had about 121 infantry battalions, 260 cavalry squadrons and 80 guns. It has been mentioned in several places that the french battalions were under strength. John Lynn suggests that the company strength of a battalion fell to about 31 men per company by this time. In a typical French battalion you would have 14 companies. So, a French battalion at Malplaqet would be about 420 men strong…or roughly 400 men if we don’t mind rounding. The French infantry arm at the battle would be about 48,000 men. Cavalry is a bit easier. There is no mention of French cavalry being understrength and cavalry was a hallmark of a French army. A typical squadron of the time would be about 120 men. Assuming 260 squadrons is correct, That works out to about 32,000 cavalry at the French disposal. So we are looking at a French army of about 80,000 men and 80 guns.
The allied side can be generalized. 128 infantry battalions is a commonly used number and several sources seem to weigh in at around the same number. An average battalion of the time is about 500 men at normal field strength. So 128 battalions is about 64,000 infantry. Cavalry, again being rather straight forward, would be based on a 120 trooper squadron. The common number of squadrons is about 252 across sources. So, the Allies would have about 30,000 cavalry at their disposal. Most sources agree that the allied gun compliment was about 100 guns. That’s 94,000 troops and 100 guns in the allied army. There are several pages that outline the deployment of each command.
The French command was broadly divided between Boufflers and Villers. Boufflers joined Villers with 63 battalions of infantry and an unknown number of squadrons of cavalry and guns. You can actually break the commands down even further with reasonably detailed deployment of the army in infantry battalions. Information on the cavalry deployment is fairly scarce but you can assume the cavalry is evenly distributed between commands.
The allied command was divided across the front in 4 commands plus one small flanking force for a total of 5 commands. Schulemberg’s assault column had 40 battalions of infantry. Lottum had 22 battalions and 30 squadrons of cavalry. Orkney had just 15 battalions (11 English) but the balance of 179 cavalry squadrons. The Prince of Orange had 30 battalions of infantry and 20 squadrons of cavalry. He originally had 49 infantry battalions and 30 cavalry squadrons but some were peeled off to make a small flanking force on the Allied right.
When using online sources for numbers of infantry battalions and cavalry squadrons, they don’t necessarily add up to the totals given. Totals are sometimes different as well. The battalion strengths are usually within 10 of any given number. The French cavalry strength has been reported by some as only 180 squadrons.