Keep in mind that the grisette is more of an idea than a specific class of woman: kind of like a Valley Girl. A Valley Girl is characterized by their colloquial way of speaking and their love of shopping, but named for the San Fernando Valley that they "come from." You can talk like a Valley Girl and shop like a Valley Girl, but are you really a Valley Girl if you aren't from the Valley? Some people say yes, some people say no.
Grisettes are tied to Bohemian culture, which suggests the Latin Quarter. Same question applies: you can act like a grisette, but are you really a grisette if you aren't partying with the students in the Latin Quarter? Maybe, maybe not. Off the top of my head, I can't remember the exact percentage, but basically every quarter (which is how rent was calculated, rather than monthly) MOST of Paris got up and changed apartments, typically you'd stay in the same neighborhood, but maybe not, it's not an exact science.
In regards to being employed doing piecework at home: grisettes could be employed in the factories, too, or work as shop assistants, seamstresses, in cafes, maybe as artist's models.
"Quand vous aurez besoin de Bahorel, capitaine, Bahorel est là! Je sais faire trébucher tous les chevaux du garde-corps avec une ficelle... Rien qu'une petite ficelle. Enfin, pensez à Bahorel du Café Musain!"