Combine sugar, water, and fennel in a small saucepan over medium-low heat. Cook until the sugar dissolves. Let cool and then strain, discarding the fennel.
Cocktail:
Pour the salt into a shallow dish.
Run a grapefruit wedge along the rim of your glass and dip into the salt, rimming the glass.
Add grapefruit juice, gin and fennel simple syrup to the glass. Stir to combine. Fill glass with ice, and stir to combine again.