Here's what our family history says:
Anton was conscripted into Napoleon’s army, and supposedly was part of the Russian campaign. It is said that he survived that campaign "because the Germans maintained discipline and retreated in rank and file." (I have never read anything in any book that supports this.) Later, he supposedly fought at Waterloo under Blucher.
If he did these things, I would guess:
Since the part of Germany where he was born was part of Greater France at the time of these events, I would guess that he was part of a regular French regiment. I know that Koblenz was the capital of the French department called Rhin-et-Moselle, and I would assume that he was conscripted through that department. I'm sure a roster of soldiers was kept at one time, but whether it survived through the centuries is a guess.
If there are rosters of soldiers kept in any archives, I would also guess that it is possible that his name was not necessarily spelled correctly. It might have been Schmitts or Schmits or any other variation.
How one could do some research on these things without knowledge of German or French or having access to the National Archives is a mystery to me.