Place the blood orange juice, sugar, cinnamon and star anise in a small pot and bring to a boil, over medium-high heat.
Once the mixture begins to boil, reduce the heat to medium/medium-low and simmer until the liquid has reduced by half, 30 to 40 minutes.
While the mixture is still hot, stir in the white wine until completely combined. Allow to cool before placing in the refrigerator to chill, at least 2 hours.
When ready to serve, place 3 tablespoons of the blood orange mixture into the bottom of each glass and top with chilled champagne (about ½ way to 2/3 of the way full). Serve!