The Army has long been infatuated with French military headgear. The Model M-1951 Field Hat appears to have been adopted from the French. It became known as the "Ridgeway Hat." Later versions in the early 60s had stiffened sides to prevent wrinkling. During the Vietnam era baseball caps and "boonie hats" became the style. To me neither looked good. Special Forces adopted the green beret in the 60s and made it look good. The Army now uses the black beret (I think the Airborne still uses maroon, and the Rangers, tan.) which to my thinking is not worn well by most soldiers.
The officers' braiding on the sides and crown of kepis is definitely a part of their rank insignia in both the North and South; though Union ones are harder to make out because they're black mohair braids on dark blue cloth caps, whereas the gold braid called for by Confederate regulations is easier to see like in the photo above of A. P. Hill. Lieutenants are supposed to have a single line of braid on the sides and forming the quatrefoil on top; captains have two; field officers ( majors, lt. col's., and colonels ) three; and generals four. This is based on Confederate practices, but both can vary from this where colonels have four and generals five.
Kepis were popular but in the realm of non-regulation items so aren't covered by regulation as much as customs based on their French prototypes. And forage caps, unlike kepis, were plain items often worn with varying or even NO decoration or insignia, especially by officers.