Here in the United States it is not all that uncommon for former military personnel to wear their DUI (distinctive unit insignia) on their bonnet alongside their clan badge. For those who maybe unfamiliar with the term, DUIs are small enamel pins that display the coat of arms of a particular unit.

I note that you live (?) in France and I am not familiar with French uniform accouterments, so don't know if there would be a direct correlation between US DUIs and something similar in the French military.