Did Henry VIII and Francis I really wrestle?

Thank you to Leah for her excellent question regarding a scene from Showtime's "The Tudors" series in which Jonathan Rhys Meyers as Henry VIII challenges  Emmanuel Leconte as Francis I to a wrestling match at the Field of Cloth of Gold meeting.
 
Did Henry VIII and Francis I really wrestle? And, if so, what happened?
 
Find out all about the history behind this scene from historian Claire Ridgway.