Place the potatoes in a medium saucepan, cover with cold water, and add a pinch of salt. Bring to a boil over medium-high heat and cook until fork-tender, about 10 minutes. Drain and let them cool slightly, then slice into halves or quarters.

In the same saucepan, bring fresh salted water to a boil. Add the green beans and cook until crisp-tender, about 2 to 4 minutes. Drain and immediately transfer them to a bowl of ice water to cool. Once cooled, drain and set aside.

Place the eggs in a saucepan and cover with cold water by about an inch. Bring to a simmer over medium-high heat, then cover, remove from heat, and let stand for 10 to 12 minutes. Drain, cool under cold running water, peel, and quarter.

In a small bowl, whisk together the white wine vinegar, minced shallot, Dijon mustard, and chopped thyme. Gradually whisk in the extra-virgin olive oil until emulsified. Season with salt and freshly ground black pepper to taste.

On a large platter or individual plates, arrange the lettuce leaves as a base. Artfully place the cooked potatoes, blanched green beans, quartered eggs, cherry tomatoes, tuna, Niçoise olives, red onion slices, and capers over the lettuce.

Drizzle the prepared vinaigrette over the assembled salad components. Serve immediately and enjoy this classic Niçoise salad.