Grate cut sides of tomato halves on small holes of a box grater into a medium bowl until only tomato skin remains in your hand; discard tomato skins. Add 6 tablespoons oil, vinegar, herbes de Provence, ½ teaspoon salt, ¼ teaspoon pepper, and garlic to grated tomato in bowl; whisk until well combined. Set vinaigrette aside.

Place 1 branzino fillet, skin side up, over rim of a plate. Gently fold fillet over the rim to pull the skin taut. Using a sharp paring knife, score only the skin by making 3 to 4 shallow slashes, being careful not to cut too deep into the fillet. Repeat scoring process with remaining 3 fillets. Sprinkle both sides of fillets evenly with 1 teaspoon salt.

Heat remaining 2 tablespoons oil in a large nonstick skillet over medium-high. Add fillets, skin side down, to skillet; using a fish spatula (see Note), gently press each fillet to flatten. Cook, undisturbed, until skin is browned and crisp, about 4 minutes. Flip fillets; cook until just cooked through, 30 seconds to 1 minute. Transfer fillets, skin side up, to plates or a platter.

While fillets cook, toss together mesclun, parsley, chives, tarragon, and, if using, chervil in a large bowl to combine. Add ⅓ cup tomato vinaigrette, remaining ½ teaspoon salt, and remaining ½ teaspoon pepper; toss well to coat.

Serve salad alongside branzino fillets, passing remaining vinaigrette (about ½ cup) at the table.