Using a vegetable peeler, peel zucchini and summer squash into ribbons. Toss zucchini, summer squash and fennel with 1 teaspoon kosher salt in a colander set inside a bowl; let stand until vegetables soften and water releases, about 20 minutes.
For sablefish, whisk together 2 quarts water, ½ cup salt, 1 tablespoon pepper, and 1 teaspoon lemon zest in a large glass bowl until salt dissolves. Add fillets and let stand at room temperature for 15 minutes.
For relish, whisk together 2 tablespoons lemon juice, 2 tablespoons vinegar, and 2 teaspoons sugar in a bowl; add 1 minced shallot, and let stand 5 minutes. Add 2 cups blackberries, 1 tablespoon basil, and 2 teaspoon lemon zest; toss to combine, then season with salt and pepper.
Preheat grill to medium-high. Brush grill grate with oil.
Remove fish from brine, pat dry with paper towels then season lightly with salt and pepper.
Place fish, skin side down, on grill grates and cook, covered, until fish naturally releases from grill, about 4 minutes. Flip and continue to cook until flesh is firm and flakes easily with a fork, about 6 more minutes (should register 125ºF); transfer to plate and let rest 5 minutes.
For vinaigrette, whisk together 2 tablespoons oil, 1 tablespoon lemon juice, 2 teaspoons vinegar, 1 grated clove garlic and ½ teaspoon lemon zest in a large bowl.
Lightly squeeze zucchini mixture to release excess water; discard water. Add squash to bowl with vinaigrette. Add ¼ cup of mixed herbs and toss to combine; season with additional salt and pepper to taste.
Transfer salad to a platter an top with grilled fish. Spoon relish over top.