In a large skillet over medium heat, combine champagne, lemon juice and shallot. Bring to a boil and then simmer for 5 minutes. With a spatula, carefully place fish fillets into skillet. If necessary, add enough additional champagne so that liquid just rises to the top edge of the fish, but does not cover it. Cover with a lid or foil and simmer for 10 minutes or until fish is firm, but not overcooked.

Carefully pour 1/2 cup of liquid from skillet into a saucepan and add cream. Bring to a boil and reduce liquid to about 1/3 cup. To serve, place fish on vegetables, rice or pasta and spoon sauce around fish.