Prepare creme fraiche ahead of time by combining heavy cream and sour cream. Cover with plastic wrap and let stand at room temperature for 12 to 24 hours.
Clean, peel and devein shrimp, leaving tails on. Pat scallops dry with paper towels and season with salt and pepper. Melt butter in a large skillet. Add lemon juice and garlic. Place shrimp and scallops in butter and saute until scallops are opaque, 3 to 4 minutes per side. Remove to a warm platter. Add Cognac or wine to pan juice. Dissolve cornstarch in stock and add along with creme fraiche to pan. Simmer until thickened. Pour sauce over shellfish and garnish with basil sprigs.