There are several school systems that serve the city of Frisco.
Frisco is served by Frisco, Lewisville, Prosper, and Little Elm school district that I know about. They may also touch Plano in a small section.
As far as open enrollment you would need to check directly with the school or school district that you would want your child to attend. In the past they were pretty strict on districting, but over the past year, many districts have changed their policy if they have space.
School districts do not always go by city boundries....they have different boundries. For example Lewisville ISD serves Lewisville, Frisco, Flower Mound, Highland Village, the Colony and perhaps some other cities as well.