I used to be a digger in the same area and these were uncommon to find - but not impossible.

I know they were found associated with several camps - mostly union - and as part of the Cane Hill/Prairie Grove campaign.

I have never associated them in NW Arkansas with a Reb site only - so I am not certain if they were Reb or Union - (or both)

Their rariety suggests that they might have been associated with one or two units only.

My best guess is that in the case of NW Arkansas - they are Federal used. The Confederates didn't get that much stuff from French sources that early in the war. The Federals were left to scour the European continent.

One note - the Union Unit that printed the "Buck and Ball" newspaper in Cane Hill on a salvaged press and type had the underheadline that "72 Caliber Gives The Rebels Hell" I kinda remember that they did have French muskets.