For line infantry (more on that later), not much that we would recognize as from current boot camp in terms of running obstacle courses and the like. Physical strength and individual initiative were much less important than learning the drill manual of how to prime, load and fire the musket to the point where it was second nature to go through the movements while tired, hungry, sleep-deprived and surrounded by clouds of black smoke. Then there's maneuver drill - how to March with "dressed ranks", how to change which direction a column is facing, how to deploy from column to line, how to form square to resist cavalry, what the commands are to do the above and what the drum cadences or bugle calls that give those signals if out of voice range. And marching. Lots and lots of route marches to test the ability to to the above after a long March and a cold night in bivouac.
For light infantry things are a little bit different, and it looks a lot more like modern fire-team training. A lot more individual or small-team initiative training about how to occupy ground, harrassment fire at officers, training for piquet or outpost duty, scouting, rearguard actions and the like.
Cavalry training was much more intense in terms of Physical training as a soldier had to go through riding school in addition to a thorough education in equine care, and then learn the particular skills of their cavalry branch. A Hussar, Light Dragoon or Chasseur a Cheval had a different role (and different horse) to a Curassier,Heavy Dragoon, Carboniere or Grenadier a Cheval. The formers training would have focused on scouting, screening, picket duty and pursuit while the latter are "shock cavalry" - big men on big horses with big swords set up to punch through lines of infantry at the critical moment.
The Physical training element of all of the above classifications is better thought of in terms of veterancy and "Elan" than our modern idea of being able to effectively train a young man straight out of school to be a good soldier. The profession of arms, for enlisted men, was not a high status occupation and attracted those with no other options, and many of those would have been borderline malnourished - not very promising specimens. The "flank companies" - the regimental specialists, took the pick of the best shots and men with some education and sense of initiative (the light company), and the bigger and more imposing men for the Grenadier company. Add to this the "Guard" units - formations with higher selection criteria, better training, higher pay and a sense of themselves as an elite, and you begin to see that there was an enormous variation between the utter "cannon fodder" and "hard as nails" units made up of older, tougher men with several campaigns under their belts.