That's the cap badge of the Gordon Highlanders, a Scottish regiment of the British Army that existed until 1994. It's the emblem of the regiment rather than a decoration, and it's extremely unlikely that from the cap badge alone you'll be able to find the soldier's surviving family - literally thousands of them were produced. I fear you may also be working from false information: nothing in the Gordon Highlanders' regimental diary suggests they ever went near Verdun. It is of course, entirely possible that they did serve alongside French troops, which led to an exchange of insignia. A good place to start might by the official Gordon Highlanders Museum.