Hull the strawberries and chop them. Slice the oranges and the limes, and then cut the orange into slices into quarters and the lime slices into halves.
Add the chopped strawberries, lime, orange, mint, and sugar to a mixing bowl or a large pitcher.
Lightly mix the fruit and sugar, cover with some plastic wrap/cling film, and place the bowl or pitcher in the fridge for about an hour (to let the sugar dissolve and the fruit release its juices). This is a good time to place your bottle of Prosecco in the fridge to chill.
Transfer the fruit (and all the juice) to a large pitcher (if you used a mixing bowl for the fruit).
(Optional) Add 2 fl oz (or 1/4 cup) of Cointreau (or orange liqueur) to the fruit and mix well.
Slowly pour the bottle of Prosecco over the fruit. You want to pour as slowly as you can to preserve the bubbles.
Mix the fruit and Prosecco (very lightly so as not to lose more of the bubbles).
Bring both the pitcher and some wine glasses or champagne glasses to the table, and make sure everyone gets some fruit with their sparkling sangria. Optionally, serve with some ice.