Well, there was some sporting use of the Lebel round. The advertisement above for the "Rival"carbine (manufactured at St Etienne, a famous French arsenal advertising"Arms for hunting, defense, target shooting and war") shows it could be had in .405 Winchester, .375 "English," (most likely the .375 Flanged Nitro Express) as well as .303 Metford, and 8mm Lebel. It advertises this rifle as suitable for hunting "Pachyderms, wildcats [Does this mean lions, tigers and leopards? The illustration shows people hunting a tiger from a howdah], and animals "shot at long distance such as chamois, eland, and reindeer," which would certainly cover a lot of territory; though I wonder where French hunters were expecting to find reindeer?
Among the "special accessories" listed are various forms of hunting ammunition, with "balle demi-blindéé" (i.e., jacketed soft points). The use of Lee Metford cartridges is interesting and likely dates this ad to the early 20th Century. The Lee-Metford round had a 215-grain bullet, and the ad says this cartridge is loaded with a bullet of "14 grams" which is 215 grains. At that time France controlled great swathes of northwestern Africa. Though there were no reindeer, various desert species, including gazelles and lions, could be found in those areas; no doubt some of the officers stationed at forts in the French Sahara would relieve the tedium and supplement their rations by hunting.
Remington (and possibly some other American makers) also loaded softpoint ammunition in 8mm Lebel for years after World War 2, presumably because enough Lebel and Berthier rifles had come into the US to make it worth their while. I remember seeing it in catalogs in my teen years. Remington's catalogs from at least as late as 1958 list it (see Page 15); that would have been about the time I was beginning to explore such things as surplus rifles.