Heat the oil in a pan. Add the carrots and sauté for approx. 2 mins. Add the rice, cook while stirring until translucent. Pour in the champagne and reduce completely. Add the bouillon little by little to the rice, stirring frequently, ensuring that the rice is covered with a small amount of liquid at all times. Simmer for approx. 35 mins. until the rice is creamy and al dente.
Sauté the shallot and garlic in butter in a wide-bottomed pan. Pour in the champagne and stock, bring to the boil, season the fish and add to the liquid. Remove the pan from the heat, cover and allow the fish to infuse (poach) for approx. 8 mins. Lift the fish from the liquid, cover and keep warm.
Reduce the liquid to approx. 3 tablespoons, remove the pan from the heat and add the butter in batches, stirring with a whisk. Return the pan to the hob a few times to barely warm the sauce; it must not boil. Stir until the sauce is creamy, season. Serve the fish and Venere rice on a pre-warmed plate, drizzle the sauce over the fillets.