Welcome to Rootschat!
Firstly, a DNA test might help determine if Andrew French was your Mother-in-Law's Father.
He served as a Private in the Durham Light Infantry 11th Battalion Service number 4454483, they may well have a photograph of him when he signed up. On the 1921 census it shows his parents Frederick and Jane Ann plus siblings Lily 1912, Norman Henry 1917, Frederick John 1920. There are family trees online with incorrect siblings, but these will be the correct ones as shown on the 1921 census. You may be able to trace a living relative from these family members, and get a photograph that way. Don't give up, as I first saw my Grandmother's photograph when I found relatives in New Zealand, I am in the UK.
Regards.