Place halibut in a baking dish large enough to lay fillets flat without overcrowding; season with zest, thyme, and chopped parsley. Cover, and refrigerate at least 4 hours or overnight.
Heat grill pan over high heat until very hot. Allow fillets to return to room temperature before cooking, about 15 minutes; just before cooking, toss fennel, fleur de sel, 3 tablespoons olive oil, and remaining 1 tablespoon lemon juice in a large bowl.
Brush fish on both sides with remaining 2 tablespoons olive oil and season with salt and pepper; place on grill, and cook, rotating once 90 degrees, until nicely colored, 2 to 3 minutes. Turn, and cook until it begins to flake and separate a little, being careful not to overcook the fish.
Gently toss arugula and herbs with fennel; season with salt and pepper. Arrange salad on a serving platter, place fish on top, and spoon salsa over halibut. Serve with remaining salsa on the side.