Preheat the oven to 425 degrees or a grill to medium-high. Season the fish with salt and pepper and drizzle with 2 tablespoons EVOO to coat.
In a bowl, combine the tomatoes, shallots and tarragon; season to taste with salt and pepper. Toss with the remaining 2 tablespoons EVOO.
Cover a baking sheet with foil. Arrange 4 piles, each with 2 lemon slices, 1 fish fillet and a quarter of the tomato-shallot mixture. Cover with another sheet of foil and pinch together on all four sides to seal the packet. Roast the fish in the oven or closed grill until opaque, 15 to 18 minutes. Open the foil packet and, using a large spatula, transfer the fish to plates. Pour the cooking juices over the fish. Pass the bread at the table for mopping.
I've made this many times and it always turns out perfect! Very easy to make and tastes great. A sure thing!!