I cannot find anything on the poem itself, but Gustave Chatain is a well known French World War One historical figure who enlisted surreptitiously at age 14, received commendations, and rose to the rank of corporal. Here he is in a publicity photo with Foch.
The first of three tales in this booklet tells a (somewhat fanciful) version of Gustave's enlistment and heroism in capturing seven Germans sleeping in a barn.
So he crept softly up the ladder and saw seven "Boches" lying fast asleep on the floor, where they had spread out beds of hay for themselves. The fearless boy brought down the butt-end of his rifle sharply on the floor and awakened them. Then they all sat up suddenly, looking very much alarmed.
....
Gustave ordered them to stand in a row as if at drill. Then he called to his companions, who were greatly amused and astonished to see seven big German soldiers holding their hands above their heads, while the gallant French boy stood looking at them with a stern, proud face. They raised a cheer for Gustave and called him a hero.
Here is another more complete retelling, in French, of Gustave's adventures.
And excerpts from Le Petie Parisien dated Jeudi 14 Septembre 1918
And another from the Journal du Loire
Fontenoy is in Belgium on the border with France, roughly 25 km NW of Mons and about halfway to Lille, and the site of a famous French victory in the War of Austrian Succession. This was the NW end of the Battle of the Frontiers in August 1914, when five German armies advancing through the Ardennes defeated French and British forces, driving them south towards Paris.
Senlis is a short distance NNE of Paris, at the very north end of French lines during the French/British victory at the Marne that drove German forces from Paris back into Belgium.
I have found two possibilities for the "Ardefine" reference in the song. Neither one quite fits, but for completeness here they are:
Gustave first joined up with a regiment of mountain troops; or in French: "Troupes alpines".
The Department due west of Paris, including Versailles, is Yvelines. This is still about 25-30 km from Senlis, but perhaps artistic licence.