Does anyone know what type of instrument this is? It looks like some type of Euphonium, but obviously very different.
The Musical Instrument Museums Online Catalog has an entry for this instrument here.
Made in Paris in 1876 by Adolphe Sax, it's simply titled "trombone with valves."
This instrument's entry on Carmentis unfortunately doesn't provide us with much extra information. Though, oddly, despite being named "valve trombone," it's classified under "valve trumpets." (Perhaps there's a distinction here among instrument classification systems that I'm not aware of.)
When manufacturing techniques got good enough for valves to be practical, there was a crazy rush to try to invent fully chromatic versions of existing brass instruments. Inventors tried lots of different schemes, and most didn't make it. This seems to be one of those failed experiments.
The one-bell-per-note is reminiscent of the Schalmei:
And the trombone range and position of the valves is reminiscent of the cavalry trombone:
Adolphe Sax did quite a bit of work experimenting with one-valve-per-note systems. They solve the inherent tuning problems of modern brass instruments, but the added weight and complexity isn't worth it.