In a small saucepan over medium heat, cook sugar, water, and fig spread, stirring occasionally, until slightly thickened and sugar is dissolved, 5 to 7 minutes. Let cool.
Make Ahead: Fig syrup can be made 1 month ahead. Store in an airtight container and refrigerate.
In a large pitcher, combine Prosecco, elderflower liqueur, and 2 oz. fig syrup. Fill with ice. Top off with club soda.
Pour spritz into wine glasses. Garnish with figs and rosemary.