Combine sugar and water in a saucepan over medium-high heat. Stir in figs, 1 cinnamon stick, and vanilla bean; bring to a boil. Boil 3 minutes. Remove from heat; cover. Steep 30 minutes.
Strain through a sieve; cool. Combine fig mixture and vodka in a chilled glass pitcher. Gently stir in Champagne just before serving.
To serve, pour into ice-filled glasses; garnish with cinnamon sticks, if desired.
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