All that I know so far about his actual war experiences is that he fought in the Great War, and that he was gassed; the lung problems this caused lasted his whole life, and he died in 1956 partly as a result of this ancient injury. See Wikipédia.
However, it is worth adding that in 1916 he published a response to Wells’s The War That Will End War (1914): L’Europe future: Réponse à M. H. G. Wells (Paris: Albin Michel, 1916). The following is a summary, with quotations translated by myself.
“The book of this English writer contains propositions that no Frenchman is able to accept, conceptions that are purely English, in regard t which is it our duty to bring forth French aspirations” (6). De La Hire accepts his proposals for redrawing the map of Central Europe. But on what he says about the Germans, and how they are not to blame for the war… “No! on all that we cannot possibly agree with H.G. Wells!” (9). The French will be conquerors in this war, and it is up to them as much as to the English to draw the new map of Europe; or, rather, to redraw the map of Europe that had been decided by numerous early treaties. We must go back to a time before the creation of Germany. Germany and Austria must be split up into principalities and republics that can never come together again. We should take a lesson from Roman times, and make the Rhine once more the boundary between France and Germany. The Balkans should be organised according to ethnography. We French would not be so bold as to assume that France should direct Europe after the war, which is what Wells assumes for the English. The four Allied powers must do it together.
I should note that there are about ten blank spaces with Censuré written on them: “Censored”. The section on the future of the Balkans has a note at the end: “The end of this section comprised about three pages on the Balkans: Censored.” I do not know enough of the circumstances to guess what Jean de La Hire would have wanted to say that was sufficiently sensitive to be censored.