For the crostini: Preheat the oven to 375 degrees F. Spread out the baguette slices in one layer on a baking sheet. Drizzle with olive oil and season with salt and pepper. Bake until lightly golden, 8 to 10 minutes.
Spread the baguette slices generously with dressing, then top with crabmeat. Sprinkle with smoked paprika and sea salt.