For the purposes of this “challenge,” when I’m transported back I somehow gain the knowledge necessary to be a soldier, and I don’t have to attend training. I’m also thrust immediately into a direct combat role. There’s no chance I somehow get lucky in a rear support role.
Possible, but not necessary follow up. While I don’t get to choose the exact role, is there a specific role I’m hoping for, such as artillery? Is there any role I’m scared of, such as cavalry? My first instinct is that being on an artillery crew would be relatively safer, especially during the Napoleonic Wars where to my understanding counter-battery fire wasn’t preferred to just pounding the enemy infantry. On the other hand, being a member of the cavalry in the Franco-Prussian sounds particularly terrifying especially as a cuirassier, charging at infantry firing back at me with long-range, accurate, bolt action rifles.
My inspiration for this post came from reading some online articles on Napoleonic casualties, one of which claimed of the 2.8 million French soldiers who fought in the wars, up to 1.4 million were killed in action, which is a staggering 50%. Reading some online articles on WW1, the fatality rates seem to be as low as possibly 10%. To me this makes the Napoleonic Wars seems much more to be the meat grinder that WW1 is often depicted as. Then I threw in the Franco-Prussian War to see how that may have compared as a decent “halfway point” in terms of both time and also technological development.
Your question is a bit complicated to answer on several grounds, but the main one is the time frame : you're supposed to serve 6 months, but if the Franco Prussian war lasted about 6 months, the other 2 lasted much longer. I'll assume that since you only mention French wars you'd be on the French side
The most obvious example would be the Napoleonic wars, which cover a span of 12-13 years (when they begin is a debate among historians) - which explains in part comparatively higher losses next to WWI. Among those years, picking the right army you could probably find periods where you wouldn't have fought a single battle in 6 months. Conversely, if you'd been part of the 1812 Russia campaign, your odds look much worse as basically a third of the army got killed, another fourth got taken prisoner and yet another fourth went AWOL over the course of 5 months
Same goes for world War I - taking part in Verdun or La Bataille de la Somme, you would not have had the same odds as some of the more "tranquil" parts of the war (be it in terms of time or location - if you were positioned in Southern France during the beginning of the war you would not have seen much fighting)
Another thing that is complicated is the "quality of life" in a way. You mention that WW1 is often mentioned as a meat grinder when casualties were kept at ~10%, this reputation is also due to the new nature of war. Wars used to be settled through massive scale open field engagements usually lasting a day at most. WWI wasn't like that - well, in the beginning maybe. But quickly the bellicists dug in, and the war went from quick bursts of enormous losses to a slow grind (excepting some offensives such as Verdun and La Somme), as lines get pounded by artillery, soldiers live and die in the mud, ever under the menace of assaults, artillery, snipers, parasites and sickness. The violence never completely stopped, and the psychological impact was very high with the first cases of PTSD ("shell shock" back then) being documented. Imagine being woken of in the middle of the night by artillery, fearing that combat gases will be dumped on your position, or that an assault will be led on your position
In most of the other two wars, in 6 months you would probably have at most a handful of field battles, with the rest of your time spent either marching of garisoning/training. Of course there are some exceptions, the main one being the campaign of Russia, but as a general rule the fighting would be concentrated in short bursts rather than being diffuse but ever present. Another difference of WWI would be that the rail and trucks would allow you to be redeployed in a matter of days rather than weeks - in the other 2 wars, armies would usually be able to routinely clear 20 to 25 km a day (without forced march)
On the other hand, with the medical progress that wasn't available during the Napoleonic wars and the franco-prussian wars (anesthesia, x ray, antisepsis - see https://www.bmj.com/content/2/2810/813.1) your odds of pulling through in case of injury would be much better (well, if you don't get tetanus but that' s another matter and this post is already long enough)
And finally, which part of the army? Well this one is a bit easier. Cavalry is a no go - even if it was able slug pretty hard as a very mobile unit that could tear a surprised of fleeing enemy to shreds, history is filled with cavalry getting completely wiped by commanders ordering an assault on a dug in position. Once cavalry loses its momentum, it's dead in the water, the risk is too great.
Infantry is better (as you said you wouldn't have a support role I'll leave out the Sapers/Génie Corps and other special corps) - although in WW1 in the beginning you would have been expected to charge into dug in German machine guns wearing your bright red pants and taking massive losses in the process. But as you said I'm expecting your best bet is the artillery. While you're making for a vulnerable target, you are away from the heat of the fight, and as a valuable asset you can expect to be protected by units more suited to combat than you are (artillery servants would typically only bear a sword and/or a pistol for self defense). In some fights (especially in WWI) you could even be out of view from the fight, and in the absence of missiles and advanced recognition techniques, even if the enemy artillery were to try to take you out it would take some time of trial and error to be able to get a decent shot at your position, often enough to allow you to relocate. Of course they're still going to try to take you out (via surprise attacks, circumventing, artillery fire or cavalry charges) because since Napoleon battles are more often than not won by the artillery, but for the same reason, no competent General would allow you to be easily be taken out (expect being positioned up a hill, with some basic fortifications like spikes, barb wire or trenches, with protection of other units and an escape route). Not such bad odds, all in all
So, closing words? If I could pick exactly the date and army, I'd probably look for an army not seeing any fighting for 6 months during the Napoleonic Wars (while I haven't checked I feel confident such a case can be found), in an artillery position (as a nice advantage, bronze cannon develop bulges when they're about to fail, so accidents during training are rare - the French military really went for steel canons only after the Franco-Prussian war, as while more resilient, steel canons do not give forewarnings before failing and metalworks were not as accurate as they are today, so artillery servants were reluctant to use them in the beginning) If I can't pick the date or location, I'd go for an artillery position in WWI as it feels on average as the safest option, despite the awful conditions of living in the trenches and the psychologically scarring nature of the fighting
Hope that helps!
The only thing I think should be called out further to Jack's thorough answer is the difference between combat casualties and those from disease. I did see he mentioned it but it should be underlined. 19th c warfare for sure saw outbreaks of all sorts (typhus, dysentery, cholera, etc) particularly during sieges as men were crowded into small areas with limited sanitary facilities, drinking water, etc.
This article at least suggests Napoleon lost 1/3 of his effectives to typhus before he even got into Russia. I suspect your time traveler is more likely to get hit by some pathogen than a combat wound.