Remove the pits from the peach and apricot and chop roughly. Place the fruit in the bowl of a food processor fitted with a steel blade. Add the lemon juice and brown sugar. Process until the fruit is puréed.

Place a fine mesh strainer over a bowl. Pour the purée through the strainer, pressing the solids with the back of a spatula to release more juice. Discard solids.

Place 1 tablespoon of the fruit purée into a champagne glass. Fill the rest of the glass with the prosecco or sparkling wine. Serve immediately.