So definitely the Coupe-Marc theory has ceased.
Further details like the well faceted long socket demanding a axe long handle versus the round short dull tube to fit a small grip add up to a different definition of this item.
Also the born weapon possibility is consensually declined.
Perhaps moving this thread to the miscelania section is the right thing, notwithstanding a flavor of weaponry that resides in its overall appearance ... to my eyes, i mean

.
It should however be nice to hear further approaches towards its definite purpose and provenance.
It will be a hard task to read the marks; some corroded area of the blade is precisely where the marks are, which makes it more difficult. It looks however that both converging words are the ame. Concerning the black paint, once it is not to give it a martial aspect, it could have been done for perservation, soon or late after its active period. Should i take it off, or just leave it as it is ?