For the sauce vierge, pour the olive oil in a non-reactive pan. Whisk in the lemon juice until well-combined. Add the chopped tomatoes, shallot and garlic.
Heat the pan over a medium heat until the sauce vierge mixture is just warmed through. Add the tarragon and season, to taste, with salt and freshly ground black pepper. Set aside.
For the coley, season the coley fillet with salt and freshly ground black pepper.
Heat the oil in a non-reactive frying pan over a medium heat. Add the seasoned coley fillets, skin-side down, and fry for 1-2 minutes until golden-brown.
Turn the fillets over using a fish slice and cook for a further 1-2 minutes, or until just cooked through.
Drizzle the lemon juice over the fish fillets and remove from the heat.
To serve, arrange the coley fillets into the centre of a serving plate. Drizzle over the tarragon sauce vierge (whisk the tarragon sauce vierge again before serving until well combined). Spoon the green salad alongside.