"Poilu" sounds perfect to me but for its use during WWI only.
Basically the soldiers that thought they would stroll throughout Berlin within a month found themselves "entranched" often without much supply except the very basics (ammo + food in that order !). Lack of razor blades, encampment in a designed area for a long time ... and the fact that hair could protect from the cold (!) all contributed that quite many French soldiers let their beards grow a little. Of course that became the host of not so pleasant beetles with time.
Veterans were still called that name after the war ended when they became a real political and social force.
So I don't mind the name at all, even though he does not "sound" great because it really had a meaning. On the other end, "poilus" would sound a bit weird in a typical Civ3 game.
But for use in a WWI scenario, that is probably the best (nick)name.
Deregatory does not mean much in these cases I guess. Red Coats, Tommies or Poilus were used by their own countries, weren't they ? Now what about Fritz for German troops ? It originately refers to Frederick II of Prussia. I am not even sure it was a hateful word though it was pretty convenient to separate "us" from "them".
If you want, I can write a pedia for it the way I did for the unit it replaces : the red-trousers XIXth century infantry.
A note on the unit: maybe it could grow a little beard to "fit" in with the nickname. About the fiery moustache, well, I guess other countries had the same habit that looks real ridiculous to us now.
It is sometimes called the Renoir (the film-maker, son of the painter) moustache.
To Padma: thanks