Place strawberries and agave syrup in a blender. Add a small splash of water if you need liquid to get the blender going. Blend until the strawberries turn into a smooth puree.
Pour the bottle of champagne into the blender and pulse 2-3 times so that the champagne is incorporated.
Transfer into baking dish and place in the freezer. After 1 hour, use a fork to scrape the frozen edges towards the center in a raking motion. Repeat 2-3 times with 1 hour intervals until the entire dish is frozen with the granita texture.