This opens up a lot of questions.
The biggest what if of this is how do the French under Napoleon respond to what, would effectively, be an “alien invasion force” that dropped in from the sky? If Napoleon reacts belligerently, a modern infantry battalion (stripped of any mechanized elements–which makes it unrealistic, but anyway) would likely, given time to prepare a defensive position and with enough ammo to have essentially unlimited, would be able to outright kill and destroy such a large number of the French they would absolutely break and retreat. So for the purposes of the OP, which was actually restricted to “how much would it take to beat back the French at Waterloo”, my answer is a battalion, assuming the French attack in force.
Now, I do think given the technology disparity, there is a potential for a Cajamarca type situation, and a group as small as a company could say, prepare some mines, utilize launched grenades, heavy automatic weapons fire, small mortars etc and the insane firepower might be enough to make the Napoleonic soldiers simply break in abject fear and mad panic, even though they might, if they to a man were unbreakable, have been able to straight up charge the position and break it apart, the human factor makes this scenario at least fairly plausible. If it was my men, I wouldn’t want to have to rely on human weakness to come back alive, so I’d still want maybe a full battalion with lots of machine guns and unlimited ammo.
A more interesting scenario is what happens if Napoleon doesn’t like what he sees and just runs away? How big a force would be required to take Napleonic era France?
That’s a lot more difficult. In that scenario, I think even a full brigade would struggle, especially given the parameters of no mechanized units. But even if you allowed them mechanized units, everything is based on logistics. You run out of gas and then transport vehicles are just interesting (to the locals) immobile curiosities. Even if you bring a mountain of ammo, how do you move it around? Soldiers can’t carry more than around a hundred pounds in an extended march, and you want them down to around 70 lb in a fight and no more. You can’t rule France from a tiny speck of land, and a brigade cannot carry mountains of ammo without a logistics chain (reliant on gas and vehicles) to move it. Food becomes a quick concern, again, even if you bring a mountain of food, you can’t just sit in one spot, you have to be able to move around in force to rule an area.
Eventually the brigade will find itself needing to live off the land. Given the fact it’s not feasible for a brigade of modern soldiers to hunt and forage itself to sufficiency this means raiding French farms and taking food. This means, most likely, necessarily splitting the brigade up a lot, in strange and hostile times. You’re going to lose guys to attrition, fuckery, misadventure etc. You can’t replace your men, the French of course, can replace theirs.
I mean to be frank, in some ways the Afghanistan the Soviets invaded was pretty damn technologically unsophisticated, and the Soviets couldn’t hold it (we helped out by sneaking more modern weapons in to them.)
Long term I think the only way to win would be to get a brigade size force to some sort of fortification and use it to lord over the local countryside. Try to convert the locals to your cause, implement feudalism if they aren’t interested. But you need a base of operations and support. Then you need to navigate the political climate of the time and try to build a base of allies and support. Get to where you can recruit men. With the typical knowledge base of a few thousand modern people, likely working with 19th century black smiths and gun smiths you can actually teach them what would be necessary to start manufacture of say, a version of a Maxim gun or etc (I am skeptical of how easy it’d be to make more modern weapons in large numbers without more precise manufacturing techniques), but if you start building up an army and can crank out a few Maxim type guns a week and train crews in their use you’ll quickly build up enough fire power to likely destroy any army sent against you, and then build up enough force projection to start building further fortresses around the country. Eventually you might be able to essentially conquer it, and remove Napoleon from power.