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Carnivals with games of chance and skill are mostly an invention of the 19th and 20th centuries. One source credits the 1893 Chicago World's Fair for the start of the traveling carnival.
A better choice for the Middle Ages would be tournaments and hastiludes, festivals showcasing various sorts of military-based games. Wikipedia's article on tournaments has a lot of information for you. Their article on hastiludes doesn't have a lot of depth, but it briefly mentions many other types of military sporting events.
You might also take a look at the various village sports of the Middle Ages like mob football. Cheese rolling is also a good fun traditional game, though it's not known how far back such an activity dates from.