Combine orange juice and peach schnapps in a pitcher; refrigerate until chilled, about 30 minutes.
Pour about 1/2 cup chilled juice mixture into six 8-ounce glasses; add 2 to 3 ice cubes to each glass. Pour 3 to 4 tablespoons champagne into each glass. Drizzle 1/2 teaspoon grenadine into each drink without stirring. Garnish each glass with a peach slice.