Bring a pot of salted water to a boil. Add the green beans and cook for 3-4 minutes, or until crisp-tender. Use a slotted spoon to transfer the beans to a bowl of ice water to stop the cooking process. Drain and set aside.
In the same pot of boiling water, add the potatoes and cook for about 10-15 minutes, or until tender when pierced with a fork. Drain and let cool slightly.
While the green beans and potatoes are cooking, place the eggs in a saucepan and cover with cold water. Bring to a boil over medium-high heat. Once boiling, remove from heat, cover, and let the eggs sit in the hot water for 10-12 minutes for hard-boiled eggs. Transfer the eggs to a bowl of ice water to cool, then peel and quarter them.
In a small bowl, whisk together the ingredients for the vinaigrette dressing: olive oil, red wine vinegar, Dijon mustard, minced garlic, salt, and pepper. Set aside.
To assemble the salad, arrange the torn lettuce leaves on a large serving platter. Arrange the cooked green beans, potatoes, halved cherry tomatoes, Niçoise olives, drained tuna, quartered hard-boiled eggs, anchovy fillets (if using), and capers on top of the lettuce in an attractive pattern.
Drizzle the vinaigrette dressing over the salad or serve it on the side.
Season the salad with salt and pepper to taste.
Serve the Nicoise Salad immediately, with crusty bread on the side if desired.