Hi,
Far from being a specialist
but, as a Froggy, I am happy to answer to this call. You are right this cloth badge is a "patte de col" or collar badge of the 16th French Territorial Infantry Regiment worn by OR from 1915 to 1917.
More informations :
https://lagrandeguerre.1fr1.net/t100...de-collet.html
Kind regards from France
Normandie18