Calpurnia is not a slave, for certain. Atticus treats her like a member of the family, and while her pay is never exactly stated in the book, we can infer that she is paid for her services.
Rather than being forcibly held and worked like a slave, Calpurnia is provided with the opportunity and choice to work for the Finches, and she is treated with dignity and respect, rather than with the common disdain shown to slaves. In fact, Calpurnia is instrumental in Scout and Jem's upbringing, serving as a mother-figure in the absence of the children's biological mother who died.
Calpurnia is most definitely not a slave. It's the south but it's the early 1930s. Slavery had been abolished almost a hundred years ago.