Melt butter in a 6-quart Dutch oven over medium-low heat. Whisk in flour until smooth. Gradually whisk in broth and wine. Bring to a boil, reduce heat, and simmer, uncovered, 20 minutes.
Meanwhile, cut top and bottom lobster shells lengthwise down the middle. Carefully separate shell halves, and gently pull lobster meat in 1 piece from shells. Cut shell halves in half crosswise, and add to broth. Cut meat in half lengthwise, then slice it crosswise into bite-size pieces. Refrigerate meat.
When shell mixture has simmered 20 minutes, add corn, potatoes, salt, and cayenne pepper. Return mixture to a boil, reduce heat, and simmer, uncovered, 12 minutes. Remove shells, and discard.
Add lobster meat, chives, and tarragon to broth mixture; simmer 6 minutes. Stir in cream, and cook 2 minutes or until thoroughly heated.