Bring a pot of water to a boil. Make a crisscross cut on the bottom of each tomato. Blanch the tomatoes for 15 seconds, then immediately shock in ice water. Peel off the skins, then halve, seed and dice the tomatoes.
Salt the tomato cooking water. Add the haricots verts and cook until well-cooked but still with some bite, about 2 minutes. Shock in ice water and set aside.
Heat some olive oil in a pan. Add the anchovy and cook for 2 to 3 minutes. Add the haricots verts and saute for 2 to 3 minutes. Season with salt.
Heat some olive oil in another pan over high heat. Pat the fish dry and sprinkle with some coriander and salt. When the pan is very hot, carefully add the fish, skin-side down, and sear until golden and crisp, about 3 minutes, pressing the fillets flat with a smaller pan. Flip the fish and cook for about 3 minutes more. Transfer to a plate to rest.
Add the shallots to the fish pan, season with salt, and cook for 2 to 3 minutes. Add the diced tomatoes, garlic and, if the pan is dry, a little more olive oil. Cook another 2 to 3 minutes. Add the wine, capers, olives and thyme. Cook until the wine is reduced by half. Taste and adjust the seasoning.
Mix the arugula and lemon juice in a small bowl.
Place the haricots verts on a plate, followed by the fish, sauce and salad.