Puree the Simple Syrup and 2 cups of the sliced peaches in a blender until smooth. Pour the puree into a glass pitcher. Add the peach liqueur and lime juice. Add the raspberries, lime slices and the remaining peach slices. Stir to blend. Refrigerate until ready to serve.
Just before serving, add the club soda and prosecco. Ladle the sangria with some of each fruit into large wine goblets and serve.
Combine the sugar and 1 cup water in a small saucepan over medium heat. Bring to a boil. Reduce the heat and simmer, stirring occasionally, until the sugar has dissolved, 5 minutes. Remove the pan from the heat and allow the syrup to cool, about 20 minutes. Strain before using.