Actually, our Civil War ended up with men marching into repeaters and Gatling guns so not terribly different. Breechloading artillery began appearing in mid-war with increasing frequency towards the end as well. If the war had gone on longer, it would have devolved into trench warfare entirely (it already did in some of the later battles) and most of the lessons were there already. Europe failed to learn anything from it and wasted many years marching men into automatic gunfire.
Yes. It has been said that we always fight the last - previous war...
So sad.
Trials were held by the U.S. Army for the Armstrong breech-loading cannon from 1862-1865, but the examples were not successful. I believe they were smoothbore.
So the Army went back to muzzle-loading cannon until 1869.
Gatling guns were still pretty much a novelty, even late in the war. It was used to good effect out west. The Spencer carbine was a good repeating rifle but there were never enough of them.
My point is, almost fifty years after our Civil war and the Franco-Prussian war, the Europeans were still using what were pretty much infantry squares and cavalry tactics.