Preheat oven to 425°.
Cut 4 (15 x 24-inch) pieces of parchment paper. Fold in half crosswise. Draw a large heart half on each piece, with the fold of the paper being the center of the heart. Cut out the heart, and open. Layer 2 orange slices, 1 lobster tail, 1 1/2 teaspoons butter, and 1 tablespoon fennel fronds near the fold of each piece of parchment. Spoon 3 tablespoons Champagne over each serving. Starting at the top of the heart, fold edges of parchment, sealing edges with narrow folds. Twist the end tip to secure tightly. Place packets on a baking sheet. Bake at 425° for 12 minutes. Remove from oven; let stand 5 minutes. Carefully open packets. Remove meat from lobster tails; coarsely chop. Return meat to lobster tail shell; place on plate. Drizzle 1 packet of juices over serving; repeat with remaining 3 lobster tails and 3 packets. Sprinkle evenly with salt.