1. Combine eggs and egg whites in a large bowl; beat vigorously with a whisk for 1 minute. Add crème fraîche, salt, and pepper; beat vigorously with a whisk for 1 minute.
2. Heat butter and oil in a large nonstick skillet over medium-high heat. Add shallot to pan; sauté 2 minutes, stirring frequently. Stir in parsley, tarragon, and thyme. Reduce heat to medium-low. Whisk egg mixture. Add egg mixture to pan; cook 1 minute, stirring occasionally. Fold in crabmeat; cook 1 minute or until eggs reach desired consistency, stirring gently. Arrange 4 baguette slices on each of 4 plates; spoon 1 cup egg mixture onto each serving. Garnish with thyme sprigs and serve with hot sauce, if desired.
Wine note: These eggs deserve a delicious sparkling wine, but the right bottle matters. A highly crisp, golden Champagne won't work as well here as a fuller-bodied, rich rosé sparkler that will complement both the crabmeat and the protein of the eggs, and look beautifully festive as well. Rosé Champagnes are very pricey; opt instead for a top-notch California rosé sparkler such as Gloria Ferrer Brut Rosé 2005 from Sonoma, California ($42). —Karen MacNeil