First things first. Courtesan is basically a fancy word for a fancy prostitute. There's more to it than that, and the history of courtesans is long and complicated, but all your need to know about Rosanette is that she's mistress to a bunch of different men: Monsieur Arnoux, Monsieur Oudry, Delmar, and of course, Frederick.
If we had to describe Rosanette in three words, we'd probably go with the following:
Sounds like a fun companion, but it's clear that Frederick is mostly with her because he can't be with Madame Arnoux. And why not pass the time in the party lifestyle? But after some initial (mostly sexual) excitement about the lady, Frederick realizes that she's kind of boring and kind of tacky—she thinks Fontainebleau is a yawn, and he's apparently not a fan of Turkish parlors complete with a hookah.
Oh, but that doesn't stop them from having a baby together. The baby dies as an infant and Frederick leaves Rosanette. So suffice it to say, things don't end on rainbows and butterflies for this poor working-class girl.