Yeah, apparently manufactured in France, but the actual cap could be from a Belgian Infantry Company or a local Luxembourg civic group.French, n'est-ce pas? Again not an expert at this, just my opinion from the manufacturers lbel.
The photo is most certainly post war US officer.
Those are Indian War era shoulder knotsCan anyone ID those shoulder boards?
A GAR hall would.I do not know why but my first impression was a railroad cap. My main reasoning was it is not US Army and not too many militia units would have that high of regimental number.