Do I need a franchise license if I have 3 business locations?

I am not licensed in your state, and it may have something called a "franchise license" but I think you are contemplating creating a franchise. A "franchise" as used in English and as used in "law" are quite different. In English it means a group of stores united by a common name and product line. In law it is a regulated legal entity which is based on a registered trademark, a licensing system, and must be registered federally and in every state where it sells or does business. It requires, among other things, audited financial statements and obtaining "franchise registration" is not a Do It Yourself project. A CPA is a well advised member of the overall team.