Prepare the Dressing: On a cutting board, use the flat side of a knife to smash the anchovy fillets, garlic, and ¼ teaspoon salt into a paste. Transfer the paste to a small bowl and whisk in the lemon juice, lemon zest, and Dijon mustard. Gradually whisk in the olive oil until emulsified. Adjust seasoning if needed and set aside.
Cook the Potatoes and Green Beans: In a medium pot, cover the potatoes with cold water by 2–3 inches and generously salt the water. Bring to a boil, reduce heat, and simmer until the potatoes are fork-tender (10–15 minutes). For haricots verts, add them to the pot during the last 1 minute of cooking. For regular green beans, add them during the last 2–3 minutes of cooking. Drain the vegetables and let them cool until warm but still manageable.
Assemble the Salad: Halve the potatoes and combine them with the haricots verts in a small bowl. Toss with some (but not all) of the dressing. Once the vegetables are completely cooled, mix in the chopped basil.
Plate the Salad: On a large platter or individual plates, arrange the dressed potatoes and green beans, radishes, tomatoes, and tuna. Scatter the olives over the top and drizzle with the remaining dressing. Garnish with freshly ground black pepper, flaky sea salt, and torn basil leaves.