Process the watermelon cubes in a blender on high until smooth. Using a fine sieve, strain out 2 cups of the watermelon juice to a large container and refrigerate for 30 minutes.
Add the vodka, triple sec and lime juice to the chilled watermelon juice. Stir until well combined.
When ready to serve, pour the drink into 4 Champagne flutes, leaving room at the top. Gently top off each flute with some Champagne.