In a large saucepan, bring cranberries and apple juice to a boil. Reduce heat and simmer, uncovered, for 10 minutes. Press through a sieve; return to the pan. Press the raspberries through the sieve; discard skins and seeds. Add to cranberry mixture; bring to a boil. Stir in the sugar, lemon juice and cinnamon; remove from the heat.
Cool for 4 minutes. Stir 1/2 cup soup into 3/4 cup cream. Return all to pan; bring to a gentle boil. Mix cornstarch with remaining cream until smooth; gradually stir into soup. Cook and stir for 2 minutes or until thickened. Serve hot or chilled. Serve with whipped cream and additional raspberries if desired.