Cut the pomegranates in half, remove the pulp and place in a large enough bowl with 4 tbsp Armagnac. Steep for 10 min.
Mix with apple juice, grenadine and preserving sugar, boil for 3 min on low heat. Cool, strain through a sieve. Fold in remaining Armagnac. Freeze in a shallow dish, stirring frequently to make the sorbet nice and fluffy.
Good trick: freeze fruit mixture in the blender jar of the food processor with the kitchen knife inserted, blending from time to time.