Preheat the oven to 350 degrees F. Line a large rimmed baking sheet with parchment paper and brush it lightly with oil.
Mix together the dill, parsley, chives and basil in a small bowl. Reserve 2 tablespoons of the mixture for the salsa and set aside.
Put the salmon on the prepared baking sheet and sprinkle all over with salt and pepper. Drizzle the top lightly with oil, then top evenly with the herb mix. Bake until just cooked through, 20 to 25 minutes.
Meanwhile, halve and peel the avocados and cut them into 1/2-inch pieces. Put the avocados in a large bowl and gently toss with the tomatoes, lemon juice, shallots, 2 tablespoons oil, 1/2 teaspoon salt and the reserved herbs. Transfer to a serving bowl.