Heat the oil and half the butter in a frying pan.
Put the fillets skin-side down in the pan and cook only on one side, basting regularly, until cooked through.
In a clean pan melt the remaining butter and cook the potatoes until golden-brown.
Add the shrimps to the pan, season with salt and pepper and add the tarragon and parsley.
Add the olive oil and lemon juice and mix through.
Take the skin off the fish.
To serve, spoon the potatoes and shrimps onto a plate, saving one tablespoon.
Lay the fish on the potatoes, top with the remaining potatoes and shrimp and pour the remaining pan juices over the top.