From the Napoleonic Wars up until the fall of Sedan, the French set military fashions, because they were perceived as the most effective fighting force (waiting for the storm of shrapnel to fall on my head). So, we copied them, the South American states copied them, from shakos and coatees in the 1810s and 1820s, up through the ACW, with our uniforms of frock or short coats and kepis. And some units adopted the uniforms of the north African Zouave and Turcos units that served with the French.
In 1871 with the French defeat at the hands of the Germans, all bets were off. Now every army introduced variations of the Pickelhaube and Waffenrock, until the conditions of the colonial wars, and rapid advances in weapons technology, made practical uniforms in drab colors more desirable. So we get our campaign shirt and hat (with the Montana pinch), and khaki and bush hats, and eventually Feldgrau in the Imperial German army.
Prost!
Brad