Jazzote is a playful, informal verb derived from "jazz". It means to play jazz, often in a casual or improvisational way, similar to "jamming" in English slang.
In the context of Serge Gainsbourg's song, it's used to describe a musician who "jazzotes" and another who "saxote" (plays the saxophone). This word is interesting because it's a creative, slightly whimsical verb that perfectly captures the musical, bohemian atmosphere of the song and the musicians it describes.
Gainsbourg turns this one into a band introduction, working through the lineup instrument by instrument and outing each player by their drug of choice instead of their solo. The horn player is "Camé à zéro" [stoned out of his mind], the piano player is tangled up in "Comme lui c'est la coco" [like him, it's the coke], and down at "Basse, c'ui qui croqu'note" [on bass, the one who chews the notes] someone is nursing a drink between phrases. By the time the drummer shows up carrying "La fleur de pavot" [the poppy flower, meaning opium], the running joke is obvious.
The title line, "Coco and co," is doing two jobs at once: it names the band and it puns on "coco," French slang for cocaine as much as it's anyone's nickname. The song closes with "Des gars du Blue Note" [some guys from the Blue Note] trading their usual vice for "Marijuana," which reads less like a twist than the last name on the list.