More often than not, farmers markets do not own the land where they operate, but rather lease or utilize it from another entity.
The Farmers Market Legal Toolkit has great information on navigating a relationship with your market host site.
Zoning & Permitting Requirements:
Consider the layout of your market. How will you manage where vendors set up, the flow of customers through the space, entertainment, etc?
Check out 2019 Homer Farmers Market Layout to get an idea of how markets can be organized.