Place the apple, orange, lime, and cranberries in the bottom of a large pitcher.
Sprinkle the brown sugar over the fruits, then use a wooden spoon or muddler to gently muddle the brown sugar together with the fruit, until the sugar has dissolved into it, 30 seconds to 1 minute.
Pour in the pomegranate juice, Grand Marnier, and red wine. Stir well to combine. Chill at least 2 hours or overnight.
Serve in pitchers with cinnamon sticks for garnish. You’ll need a long spoon to serve the fruit, or you can remove the fruit to a bowl and have guests add it to their glasses as desired. The sangria will last, refrigerated, for several days.