1. Combine the wine and sugar in a saucepan and bring to a simmer, stirring until the sugar is dissolved, then cool.
2. Puree the honeydew and tarragon in a blender, then strain through a fine-mesh sieve into a mixing bowl. Combine the wine, honeydew juice, lemon juice, and a pinch of salt, then transfer to a square baking dish. Put in the freezer until firm, scraping and stirring with a fork every 30 minutes until the mixture is slushy, about 2 hours. Serve garnished with tarragon leaves or sprigs.
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