During the Medieval Period organized athletics, as they had been enjoyed by the Greeks and Romans, all but disappeared.
The Feudal System of knights paying homage to their liege lords, with military service, was the basis for jousting tournaments. Boys and men spent much of their time on the practice fields perfecting the skills that were needed in battle. These included wrestling and hand to hand combat, swordsmanship and horsemanship. The armor, chain mail and padding worn in battle was extremely heavy, as well, and required excellent physical condition for a man to be effective in battle. The reason for all the training and exercise, though, was war, not sport.
Life for the vast majority of the people was very physically demanding. Imagine farming without machinery, done with hand tools and the strength of your body! Imagine running a home and feeding a family without running water, having to carry water, heat and cook with wood or peat, washing clothes by hand. As you can imagine, for most people there was no need for any extra exercise. In fact, when Medieval burial sites have been excavated, it was easy to tell whether the remains were that of nobles or common folk by the size of the bones. The heavier the bones, the harder the person worked. People used their bodies and worked hard just to survive.
Games did exist in the Medieval Period, but tended to be more like today's "parlor" games. There were board games as far back as ancient Egypt. There is historical evidence that forms of backgammon, cribbage, chess and checkers did exist during the Middle Ages. There were also dice made of stone, wood and knuckle bones.
With the coming of the Renaissance and the rise of the Middle Class, people had more leisure time. Games such as early forms of bowling and tennis were played. Children, and adults, played with balls made of animal bladders, cloth and wood. Hobby horses, dolls, toy soldiers made from clay and wood; and small wooden "play" swords were also known to exist at the time, for children.
Card games were also introduced into Europe during the Renaissance; and became popular. With increased leisure time the previously existing board games also became increasingly popular. Swordsmanship, previously used in battle, was refined into the sport of Fencing, with rules and specific moves.
Organized sports as we know it today did not exist, but people have always enjoyed competition in whatever ways were available.