In a large pitcher or punch bowl, combine the red wine, sugar, and brandy.
Stir until the sugar is mostly dissolved.
Cut two of the oranges and one of the lemons into wedges.
Squeeze the juice from each wedge directly into the wine mixture, then drop the spent fruit wedges into the pitcher. Give it another good stir.
Cover the pitcher and chill in the refrigerator for at least 2 hours, or up to 8 hours, to allow the flavors to meld together. The longer it sits, the more flavorful it will become.
Just before serving, thinly slice the remaining orange and lemon.
Stir the Triple Sec into the chilled sangria. You can remove the old, squeezed fruit for a cleaner look, or leave it in for a more rustic feel.
Add the fresh orange and lemon slices to the pitcher along with a generous amount of ice.
Top with club soda to your desired level of fizziness, give it one final, gentle stir, and serve immediately.
Add other fruits like sliced apples, peaches, or berries for extra flavor and color.
Add heartier fruits like apples early on, and softer fruits like berries just before serving.