Place the potatoes in a saucepan and cover with cold water. Add a pinch of salt. Bring to a boil over medium-high heat and cook for about 15-20 minutes, or until tender when pierced with a fork. Drain and let them cool slightly. Once cooled, cut them into quarters.
Place the eggs in a saucepan and cover with water. Bring to a boil, then reduce the heat to a gentle simmer. Cook for 8-10 minutes for hard-boiled eggs. Transfer to a bowl of ice water to cool quickly, then peel and cut them in half.
In a pot of boiling salted water, blanch the green beans for about 2-3 minutes, or until they turn bright green and are crisp-tender. Drain and transfer to a bowl of ice water to stop the cooking process. Drain again and set aside.
In a small bowl, whisk together the olive oil, red wine vinegar, minced garlic, Dijon mustard, salt, and pepper. Adjust seasoning to taste.
On a large serving platter or individual plates, arrange the mixed salad greens. Arrange the cooked potatoes, hard-boiled eggs, blanched green beans, cherry tomatoes, Nicoise olives, and red onion on top of the greens. Add the flaked tuna and anchovy fillets (if using) to the salad .Drizzle the dressing evenly over the salad.
Garnish the salad with fresh basil leaves, if desired. Serve immediately, with a crusty baguette or French bread on the side.