Stir the sugar and water in a large saucepan over medium heat until the sugar dissolves, about 5 minutes. Cool completely.
Puree the peaches and orange peel in a blender with 1/2 cup of the sugar syrup until smooth. Strain through a fine-meshed strainer and into a bowl. Cover and refrigerate. In a clean blender puree the strawberries with 1/3 cup of the sugar syrup until smooth. Strain through a clean fine-meshed strainer and into another bowl. Discard the seeds. Puree the blueberries in a clean blender with 1/3 cup of the sugar syrup until smooth. Strain through a clean fine-meshed strainer and into a third bowl. Discard the seeds and solids. Pour each of the purees into clear glass bowls or small pitchers.
For each serving, pour 2 to 4 tablespoons of the desired fruit puree into a Champagne flute. Slowly pour enough Prosecco into the flute to fill. Gently stir to blend. Garnish with the whole berries, as desired, and serve.
Do-Ahead Tip: The fruit purees can each be made 1 day ahead. Cover separately and refrigerate.