In saucepan over medium-high heat, bring sugar and water to boil, stirring with wooden spoon until sugar is dissolved; remove from heat and let cool.
Whisk guava pulp, crème fraiche and lime zest into sugar syrup until fully incorporated.
Process mixture in ice cream maker, according to manufacturer’s instructions. Store in freezer. When ready to serve, scoop into dessert bowls and garnish with mint sprigs.