i had a similar badge (below) ---genuine 25 %....
for me it's (perhaps)a military provost staff corps (2sd modele 1910/1936) also worn by barrack wardens betwen 1912 to 1937....
i take that from a french article in "militaria magazine" (french) articles on ww1 cap badge. in this article they also speak about the 1st modele with the wreat...
if you want i can send you the scan of the 2 pages (1.6 mo each) ---