Since you know that he was part of the 4th Division, do you have his discharge papers which would show what part of the 4th he was in. (4th Supply Train, 4th Ammunition Train or 4th Engr Train or 4th Sanitary Train - Ambulancewould be first choices)
The 4th Div arrived in France from Apr 21 to Jun 9, 1918, as didmost of the US Army units. With that info search for the specific actions in which the 4th was involved. A History of the 4th Divison could be available in many libraries.Also locate a copy of "Order of Battle of the United States Land Forces in the World War - Divisions". A summary of the activities of all divisions is there.