Combine the currant juice and sugar in a small saucepan and bring to a simmer over low heat. Cook, stirring occasionally, until the sugar dissolves, about 4 minutes. Transfer to an 8-inch-square stainless-steel or glass baking dish and let cool completely; stir in the grape juice.
Freeze until ice crystals begin forming around the edges, about 45 minutes. Use a fork to scrape the crystals toward the center of the pan, then continue freezing, scraping every 30 minutes, until frozen, about 4 hours.