Excellent choice! This is one funny song, and you did it justice. Really a fun and pleasant read.
You missed a few bits of colourful slang, but I won't hold that against you.

feignants -> lazy, slack, lazybones...

de son dodo -> to be honest I'm not familiar with that use of the word, but the meaning must be "bed".
"dodo" is a kid's word for "sleep", used in the famous "métro, boulot, dodo" (subway, work, sleep), a symbol of the daily grind.

les tifs -> like "les cheveux"

l'air pensif -> more like "looking in wonder at his feet". Trying to collect his thoughts, not looking very bright, basically :)
"r'gardant" is "regardant" with the "e" muted. I find these quotes mightily annoying myself, that's a great example of how they can really become confusing.

Restez pucell' -> again these damn quotes, it's "pucelle" (a virgin). "stay a virgin living at your dad's"

bougnat -> the owner of a bar/café

Raise a monkey, or a cat -> rather "breed monkeys or cats" :)

Levez la patte -> "patte" is a pesky word that can mean "hand" or "leg" depending on the context. Here it's about a dancer raising her leg, but "lever la patte" is rather used for cabaret dancers like in the Moulin Rouge, and coincidentally to describe an urinating dog :D

gagas -> from "gâteux" (senile, soft in the head). Dotards, or rather old lecherous swines, in that context :D

Soyez radeuse av'nue du Bois -> "radeuse" is a whore, "av'nue" is "avenue" (yet another damn confusing quote), i.e. "be a whore (working) on the Avenue du Bois". The "bois de Boulogne" is a wood near Paris famous for hosting lots of prostitutes. Or it's just a funny name he made up for the rhyme.

homme gêné -> lit. "an embarrassed man", "a man that feels awkward" but you could also say "did you see a man awkwardly come home with some lipstick on his collar" or something like that.

Du rouge à lèvres sur son col / Du flageolant dans la guibole -> the layout is wrong, it's still about the same guy, with some lipstick on his collar *and* passably tipsy :)
That sent you off track for the next sentence, which starts talking about a different guy.

Se frotter avec insistance / Sur un' petite fleur d'innocence -> lit. "rubbing himself insistently against a small flower of innocence".
A slightly younger version of the aforementioned old swines, hitting on a young innocent girl, basically :)

"prendre la braise" -> to be honest I don't know that expression, but [@Jadis] could surely help.

about note #3, I see no pun in French either. "l'artiche" is just one of the many slang words for "dough" (they keep the dough [for themselves]). "stingy" seems perfectly good to me. Or "skinflints" maybe? Whatever sounds funnier.

Avez-vous vu à votre bras
Un maigrichon aux yeux de rat
Friser ses trois poils de moustache
Et se redresser, l'air bravache -> again the layout is a disaster. It's a new stanza, beginning with the picture of a skinny, rat-eyed guy walking arm in arm with the girl, twirling a tip of his pitiful moustache and straightening up in a pathetic attempt at swaggering.
That should get you unstuck, let me know if you need some vocabulary.

Changez d'amant quat' fois par mois -> it's still an imperative, lit. "change your lover four times in a month" (take a new lover every week)

wonderful life it could be -> it will be (provided the girl stashed enough dough)