Sprinkle the fish with salt and pepper and place each on a double rectangle of foil. Top with the arugula, half the lemon slices and the fennel. Sprinkle the outside of the fish with salt and pepper, drizzle lightly with olive oil and splash each with some wine. Enclose each fish in the foil, sealing to make a packet. Wrap each fish one more time with foil.
Place the foil packets on the grill and cook for 25 to 30 minutes.
Remove the skin and fillet the fish from the bones. Serve on a platter with the remaining lemon slices. Garnish with the arugula and fennel. Squeeze a little lemon juice on top of the fish, just enough to taste.