1. Combine first 3 ingredients in a saucepan. Bring to a boil; stir until sugar dissolves. Let stand 15 minutes. Pour through a fine sieve into a bowl; discard solids.
2. Cook peaches in a large pot of boiling water for 1 minute. Place peaches in a bowl of ice water until cool. Peel peaches; remove pits and chop flesh. Place chopped peaches and lemon juice in a blender; process until smooth. Stir peach mixture and salt into basil mixture. Chill 1 hour.
3. Pour peach mixture into the freezer can of an ice-cream freezer; freeze according to manufacturer's instructions. Spoon sorbet into a freezer-safe container; cover and freeze until firm. Serve with raspberries. Garnish with basil sprigs, if desired.