Make the sauce several hours or the night before. In a non-reactive mixing bowl, stir together the chopped tomatoes, shallots, basil, lemon zest, olive oil, vinegar, chives, and tarragon. Season to taste with salt, pepper, and a little cayenne. Cover the bowl and leave at room temperature to marinate for several hours or overnight (if your kitchen is very hot, refrigerate.).
About 1/2 hour before serving time, preheat the oven to 400 degrees F. Cover a baking sheet with foil and lightly oil the foil with olive oil. When the oven is hot, switch it to its broiler function. Brush the salmon fillets with olive oil, season them with salt and pepper, and arrange them on a baking sheet. Place the salmon under the broiler about 2 inches from the flame and cook until done the top is very lightly browned and the flesh is still slightly pink in the center, 7 to 8 minutes. Meanwhile, taste the sauce and, if necessary, adjust the seasonings to taste.
Spoon a generous amount of the sauce onto the middle of each of 6 heated serving plates. Place the salmon fillets on top of the sauce. Top each fillet with a basil sprig. Serve immediately, passing any remaining sauce separately.