Position a rack in the top third of the oven and pre-heat to 475°F.
On a large rimmed baking sheet, toss the potatoes, haricot verts, tomatoes, olives, shallots, garlic, thyme and rosemary with 1/4 cup EVOO. Season with sea salt and pepper; spread evenly on a baking sheet. Roast, stirring once, until the potatoes are tender, about 25 minutes.
Meanwhile, heat a grill or griddle pan over medium-high. Season the tuna with herbes de Provence, sea salt and pepper. Drizzle the pan with the remaining 1 tablespoon EVOO. Add the lemons, cut-side down, and cook until browned, 3-5 minutes. Transfer to a plate. Add the tuna and cook to desired doneness, about 2 minutes per side for pink centers and 3 minutes per side for opaque centers.
Serve the tuna with the vegetables and lemons.