I don't know the answer but it is possible that "1 G" stands for "1er Régiment du Génie". "1 Gr." would, IMO, be used for "1er Régiment des Grenadiers" (my dad was one in WWI). Hereby also a drawing that made me think it's indeed the mentioning of a regiment, in this case "1 CH. CH" ("1er Chasseurs à Cheval", I served with them in the mid-sixties). "Gendarmerie" wouldn't be my first thought but I've been wrong before. Just my 2 cents.
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