In a saucepan, bring water, strawberries, sugar, lemon juice, and Champagne to a boil. Let simmer for 10 minutes, then add mint leaves. Let cool to room temperature.
Blend together with an immersion blender or in a standing blender, then strain through a sieve. Chill in the refrigerator, covered, for 3 hours.
Serve in soup bowls with a scoop of ice cream or sorbet. Garnish with mint leaves.