In a medium saucepan, combine half of the blackberries with the sugar and 1/3 cup of water and bring to a simmer. Cook over moderate heat, stirring occasionally, until the sugar is dissolved and the liquid is slightly thickened, about 5 minutes. Transfer the mixture to a food processor or blender. Add the remaining blackberries and chambord (if using) and puree until smooth.

Strain the puree through a fine sieve set over a large bowl. Add the Champagne and lemon juice and mix well. Pour the mixture into a 9-by-13-inch glass or stainless steel baking dish.

Freeze the granita for 2 hours. Scrape the frozen edges into the center. Freeze for another 3 hours, scraping hourly, until the granita is icy and flaky.