Hi there -- the French victory medal was actually called the Inter-Allied Victory Medal and awarded to all soldiers who had served for at least three months between 1914-1918 in the war zone, as well as nurses, some POWs and others, and was awarded to Allied personnel regardless of nationality.

Also, if you'd like to find out more about your great-grandfather's service, our Guide on Military Identification may be of use to you. It provides a number of different resources, including how to request service records from a number of national agencies around the world, as well as graphical aids to assist in deciphering rank, unit, and other forms of badges or insignia. While the users here may still be able to lend you more assistance, hopefully this will provide a good place to start!