This Champagne cocktail takes its inspiration from the Italian bellini.
Cut off 1/4 inch of peel from 6 oranges at the stem end, and discard. Place trimmed oranges in an 8-quart stockpot; cover with 4 quarts water. Cut a circle from parchment paper, and place over the surface. Bring to a boil. Reduce heat and simmer, uncovered, 2 hours.
Remove trimmed oranges; place upside down on a wire rack to drain (save parchment round for later use). When cool enough to handle, scoop out flesh with a spoon (do not puncture orange skin). Discard flesh and cooking water.
Combine sugar and 8 cups water in a clean stockpot. Bring to a boil over medium-high heat. Cook until syrup reaches 220 degrees on candy thermometer. Add orange shells, and reduce heat. Cover with reserved parchment round, and simmer for at least 1 hour, occasionally turning gently. Oranges will be unevenly translucent. Turn off heat, and let cool in syrup until completely translucent, about 2 hours. Gently lift oranges from syrup and place upside down on a rack over a baking sheet. Let dry overnight. Store in an airtight container lined with parchment paper.
With a channel knife, remove curls of zest from remaining oranges for garnish; then cut away peel and pith of remaining oranges and grapefruit, and cut along membranes to segment the fruit. Place each candied orange in a Champagne coupe, and fill with citrus segments. Top with 1/4 teaspoon coarse sanding sugar, and add Champagne (about 3 ounces). Garnish with citrus-peel curls.