Combine apple juice and 1 cinnamon stick in a large heavy pot. Bring to a boil, reduce heat, add orange slices, and simmer uncovered 10 minutes. Strain into a heatproof bowl and press on oranges to extract juices; discard oranges (save cinnamon stick). Stir in sugar, tequila, and dried fruit. Let steep 1 minute, covered.
Divide dried and fresh fruit among 8 heatproof glasses or cups and ladle in punch. Add a cinnamon stick to each.