Bring 6 cups water to a boil in a medium saucepan. Add the tapioca, reduce the heat to medium and cook, stirring occasionally, until tender, about 15 minutes. Strain the tapioca in a large sieve, and rinse under cold running water until cold. Spoon the tapioca into a 3-quart pitcher.
Add the wine, grape juice and liqueur to the pitcher, and stir to combine. Add the tarragon and peaches, and cover the pitcher with plastic wrap. Refrigerate the sangria to chill, at least 4 hours up to overnight.
To serve, fill 8 glasses halfway with ice. Stir the sangria to redistribute the tapioca, then pour the sangria, fruit, and tapioca into each glass.
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