Combine apple juice, lemon juice, orange zest, and cinnamon sticks in a medium saucepan.

Bring the mixture to a boil and then reduce heat to simmer for 10 minutes, uncovered.

Remove from heat and allow to cool to room temperature.

In a large serving bowl, combine the chopped apples, pineapple, orange sections, and grapes.

Remove the cinnamon sticks from the cooled apple juice mixture.

Pour the apple juice mixture over the prepared fruit in the serving bowl.

Chill the fruit cocktail in the refrigerator before serving.