In a bowl, whisk 1/4 cup of the mayonnaise with 1/2 teaspoon of the curry paste; chill.
In another bowl, combine the remaining mayonnaise with the crème fraîche, lemon juice, chives, parsley, tarragon and diced apple. Season with salt and pepper. Fold in the crab, form into 4 patties and coat with the panko. Transfer the crab cakes to a lightly oiled baking sheet; chill.
Preheat the broiler and position a rack 8 inches from the heat. Drizzle the crab cakes with 2 tablespoons of the oil and broil for about 12 minutes, turning once, until golden and crisp. Transfer the crab cakes to plates.
In a medium bowl, whisk the remaining 2 tablespoons of oil with the 1/2 teaspoon of curry paste and the vinegar and season with salt and pepper. Add the apple matchsticks and cilantro and toss. Serve the crab cakes with the curry mayonnaise and apple salad.