Zouave and Sophisticated: Why do monkeys dress that way?

This morning I was rolling cigarettes and because I was rolling Zig-Zag tobacco, I put on a fez. Kim came in and said, "you're wearing a fez because of the man on the can." (Long ago, she stopped wondering why I own such odd things to begin with, and in fact, bought me the aforementioned hat.) "That's right," I said, because of the Zouave." This is the second time the subject of Zouaves has come up in the past week.
The first time was when I read that it was Zuoaves who first popularized absinthe in France. And it got me to wondering if Zouaves had any other impact on us besides for licorice liquor, and inventing the cigarette.

The only other thing I could come up with is monkeys. Monkeys, especially of the organ grinder variety, are often dressed as Zouaves. Why is this? (When I was a kid I thought they were dressed like bellhops.) Did a regiment have a monkey as a mascot? Were Zouaves slurred as monkeys? I don't know and I couldn't find anything on the subject at all. If you know, please drop me a line in the comments section. And if you can think of any other Zouave references in popular culture, please comment on that too.

During that seeking for lions which he never found, the dreadful Tartarin roamed from douar to douar on the immense plain of the Shelliff, through the odd but formidable French Algeria, where the old Oriental perfumes are complicated by a strong blend of absinthe and the barracks, Abraham and "the Zouzou" mingled, something fairy-tale-like and simply burlesque, like a page of the Old Testament related by Tommy Atkins. - Alphonse Daudet (1872)

Monkey picture filched from Geek Chic