In a medium saucepan, bring figs, sugar, and 1½ cups water to a boil over medium-high heat. Reduce heat to medium-low, simmer, stirring occasionally, until figs begin to break down, 5 to 7 minutes. Remove from heat and steep for 20 minutes. Strain through a fine-mesh sieve.

For each serving, fill glass with ice, pour in ¼ cup simple syrup, ½ cup wine, 1½ teaspoons lime juice, and about ¼ cup sparkling water. Garnish with lime and mint.