At the beginning of the 19th Century, Napoleon was seen as "the greatest military leader of recent times," and French was naturally the language to be learned in order to facilitate the study of Napoleon and his strategy and tactics. In the process, French terms for military ranks, units, movements, weaponry, etc were reaffirmed as "the correct terms" for universal understanding (and new French terms were incorporated into American military terminology.)
The following link: a publication provided to American soldiers deployed to Europe in 1917 (with attention being directed to French Military Terms on pages 7 - 16.)
https://babel.hathitrust.org/cgi/pt?id=uc1.$b260555;view=1up;seq=5 French for the Army and Navy (1917).
[And for a brief discussion of how French military tactics influenced the course of instruction at West Point: https://www.historynet.com/french-lessons-west-point.htm French Lessons at West Point, initially taught by Francis De Masson from 1803 - 1812 and making certain that military terms such as bastion, glacis and abatis were incorporated, and followed later by empennage, fuselage, nacelle, and aileron (when the airplane entered service.]