Soak raisins in a bowl of hot water until soft, 5 to 10 minutes. Drain.
Heat olive oil in a large saucepan over medium heat. Cook and stir onion and garlic in the hot oil until fragrant, about 5 minutes. Stir in raisins, rice, and salt; cook and stir until rice is coated with oil, about 3 minutes.
Pour boiling water and Champagne into the saucepan. Cover and cook until liquid is absorbed and rice is tender, about 20 minutes.
Place dried apricots in a small saucepan and cover with water. Bring to a boil; simmer until soft, about 5 minutes. Drain and cool slightly, about 5 minutes. Cut into strips.
Place grated carrot in a small bowl and cover with boiling water. Season with salt. Let soak until softened, about 5 minutes. Drain.
Melt butter in a saucepan over medium heat. Stir in apricot strips and sun-dried tomatoes; cook for 2 minutes.
Fold apricot strips and sun-dried tomatoes into the cooked rice. Pile rice onto a serving platter; garnish with grated carrot.