With a rubber spatula, mix together the creme fraiche, basil, chives, tarragon, olive oil, lemon zest, lemon juice and salt in a medium bowl. Add the crabmeat and gently fold it into the herb dressing until the crab is coated and the herbs are evenly distributed. Top each crostini with a tablespoon of the crab mixture.
The crab salad can be made up to 1 day ahead and stored, tightly covered, in the refrigerator. To make crostini, brush sixteen 1/4-inch-thick slices of baguette on both sides with 3 tablespoons olive oil and sprinkle with 1/2 teaspoon salt. Place on a rimmed baking sheet and bake in a 400-degree oven for 10 minutes, rotating halfway through.