I am creating a museum that would allow a game character to walk around and interact. What would happen if I got a large number of players in the free game? What is the Epic fee structure in this circumstance?
Epic has its commercial terms listed in their FAQ in a very comprehensive manner: Frequently Asked Questions - Unreal Engine
Free titles are free 
Epic only collects on products that earn a certain threshold per quarter.
Good luck with your project! Hope this helped.
Excellent! Thank you so much.