In a small saucepan, heat the sugar and water. Stir until sugar is dissolved and liquid is completely clear, about 3 minutes. Remove from heat and let cool completely.
Cut the peaches and watermelon into 2" chunks and puree in a food processor or blender. Add grated ginger and lemon juice. Pour into an airtight container and add the wine and cooled sugar water, and stir. Chill in a refrigerator 2 hours.
Pour the mixture into an ice cream maker and follow your machine’s instructions for making sorbet. Freeze in an airtight container about 1 hour or so before serving to “set” the sorbet. OR Alternatively if you do not have an ice cream maker, place the airtight container in the freezer for 2 hours and every half hour stir it all up vigorously. Then let set an hour after that 4th stir. It won't be as smooth as with the machine, but just as delicious.