Combine the raisins or currants and rum and set aside to soak. Combine the sugar and ½ cup water in a saucepan and bring to a boil, stirring. Cool.
Mix together the sugar syrup, fromage blanc or yogurt, lemon juice, and 1 cup water. Freeze in an ice cream maker according to the manufacturer’s directions; when the mixture is nearly frozen, add the soaked raisins