Place sliced peaches and blueberries in a large pitcher.
Pour peach syrup, rum, wine, and sparkling water over the top of the fruit. Stir and refrigerate until ready to serve, at least 2 hours, until cold.
Notes
The longer the sangria sits, the more color will develop in the sangria. If you like the color, I recommend making it a day ahead and leaving the sparkling water out until right before serving.