Mrs Walsh said they removed the back of the frame to try to find out more about him, but with no luck.
The students tried to find him on the internet and had turned up at least two E Thomas' from the Welsh Guard, but were not convinced either were their man.
Student Nicolas Dault said they found two E Thomas' who had died on the same day in the same battle, but many soldiers of the time looked the same.
His classmate Jack Gallon said he could have been part of a mortar team.
The class agreed the man looked very young and was probably convinced to join up after listening to British propaganda of the time that said soldiers would be "back before Christmas".
"It's a big mystery, but it's been a lot of fun trying to solve it," Nicolas said.
Sophie Bye said they had learned a lot about the war and how women left behind had to do the work of both men and women. She said it would have been terrible watching the men head off to battle.
"It would be really cool to return [the photo] to his family, it might make them really happy and it could be the only photo they have of him," she said.
Mrs Walsh said anyone who could help her class find any information about Private Thomas could contact her at the school.