Combine the fish, crème fraîche, chives, lemon zest and juice, cayenne pepper, and ¼ teaspoon black pepper in a medium bowl. Cover and refrigerate for up to 2 days.
Drizzle the sourdough toasts with the oil and cut into triangles. Spread the fish on the toasts. Sprinkle with chives and serve with the lemon wedges on the side.