The best way would be to find his file in the military archives. Since he was born in Lyon, you have to search for him from the Recrutement Militaire at the Archives du Rhône website.
Année de recrutement (classe) would be the year he turned 20 (so 1906) then pick a bureau de recrutement (I would start with Lyon Central). Then browse the Répertoire Alphabétique (the first document in the list of results) for him. On page 15 there is a Joseph Louis Henri Gardet with the matricule number 1334. Would that be him? If you think so, note down the number and look for the file in the "Registre Matricule" document that contains files 1001 to 1500. Joseph Louis Henri is on slide 515. Is this your Louis? If it is not, you'll have to look for him in Class 1907 and/or other Lyon recruitment offices.
According to the matricule file, Louis Gardet did not receive any decorations. I believe if he had one, it probably should be listed there, and if you look at the next file, on the following page, this is a soldier who did receive the Croix de Guerre. You can see it in the "Blessures, Actions d'éclat, décorations" frame.
But, even when there is no decoration listed on the file, there is still a wealth of interesting information on the file - birth details, names of parents, details of his military affectations, where he lived, that he was injured, what he looked like (height, color of hair and eyes...) etc.