Process the rose petals with the sugar in a food processor until the mixture turns into a smooth paste, about 30 seconds; stop to scrape down the sides as necessary. Add 1/2 cup of the water and process for about 10 seconds. Add the remaining 2 1/2 cups water, the lemon juice, Champagne, and rose water if using. Pour the liquid through a fine sieve. Freeze the mixture in an ice cream maker according to the manufacturer's directions.