Pour the juice into a 9x13" pan and freeze for 2-3 hours. Depending on the size of your pan, the granita will freeze at a different speed (ie a bigger pan means the juice will freeze faster). Every 20-30 minutes, using a fork, scrape the ice (all of it, not just the top layer), to make sure that the juice doesn't freeze into one block.
In a medium bowl, whip the cream until soft peaks form. Add the almond extract, then mix until combined.
Divide the granita between 6 champagne glasses, then top with the whipped cream. Serve immediately.