French military brothels seem to be about 1870 to about 1970, usually identfied as "BMC".
I am surprised that Napoléon did not regularize the practice of camp followers, giving them unique uniforms, rank distinctions and catchy unit names -- humorous examples of which I shall not be the first to suggest.

"bordel mobile de campagne"
"bordel militaire de campagne"
"bordel militaire controlé"
"maison de tolerance"
"quartier reservé"
"la boîte à bonbons"

Anyway, when the French got around to actually having mobile brothels, several decade later, the word used was indeed "mobile" not "ambulant", for what it's worth.