6 teaspoons red raspberry liqueur, such as Chambord
One 750-ml bottle sparkling wine, such as Prosecco, chilled
Peach slices, raspberries, and fresh mint sprigs, for garnish
Place a 9-inch diameter metal cake pan in the freezer to chill while preparing the peaches.
Bring a large saucepan of water to a boil over high heat. Place a large bowl of ice water next to the stove. Add the peaches to the boiling water and cook just until their skins loosen, about 30 seconds. Using a slotted spoon, transfer the peaches to the ice water and let stand until cooled. Drain the peaches. Peel, pit, and coarsely chop the peaches.
In a food processor fitted with the metal chopping blade (or in a blender, working in batches), combine the peaches, sugar, and lemon juice and process until pureed. Pour into the chilled cake pan. Freeze until the edges of the puree are icy, about 2 hours.
Using a metal spoon, stir the puree to combine the icy and unfrozen parts together. Freeze until the edges are icy again, about 1 hour more. Repeat the stirring, and freeze until the puree is slushy, about 1 hour more. (The frozen peach slush can be covered and frozen for up to 1 day.)
Scoop equal amounts of the slush into 6 champagne flutes. Top each with 1 teaspoon raspberry liqueur. Slowly pour the sparkling wine into the flutes (you may have to nudge the peach slush with a long spoon to be sure that the wine reaches the bottom of the glass). Garnish each with a peach slice, raspberries, and a mint sprig and serve chilled, with long spoons to eat the slush, if you wish.