For the mint simple syrup:
In a small saucepan, combine the sugar, water, and mint over medium heat. Bring to a boil, reduce heat, and simmer for 5 minutes, stirring occasionally, until the sugar has dissolved. Remove the pan from the heat and allow the syrup to cool for 20 minutes. Strain and chill before using.
For the sangria:
In a large jug, combine the prosecco, orange juice, mint simple syrup, lemon zest, and lime zest. Add the sliced strawberries, lemon slices, lime slices, and mint sprigs.
Fill glasses with crushed ice and pour the sangria over the top. Serve immediately.