Fill a large pot with water, cover it, and set it over high heat to bring it to a boil. Set a medium bowl of cold water near the stove for the eggs.

In a large mixing bowl, whisk together the olive oil, Dijon mustard, red wine vinegar, the juice from half the lemon, 1/2 teaspoon of the salt, and the black pepper until the dressing looks smooth.

Add the sliced red onion to the mixing bowl and toss it in the dressing. Let it sit while you cook the rest so it softens and loses some of its sharp bite.

Put the eggs into a small saucepan and cover them with cold water by about 1 inch. Set the saucepan over high heat.

When the water in the saucepan reaches a full boil, lower the heat so the water bubbles gently. Cook the eggs for 7 minutes for soft but set yolks, or 9 minutes for firm yolks.

Lift the eggs out of the saucepan with a spoon and put them into the bowl of cold water. Let them cool for about 5 minutes.

When the water in the large pot is boiling, add the potatoes and a generous pinch of salt. Cook the potatoes for 12 to 15 minutes, until a fork slides in easily.

Use a slotted spoon to transfer the potatoes from the pot to a colander. Leave the water in the pot and keep it over high heat.

Put the green beans into the same pot of boiling water. Cook them for 3 to 4 minutes, until they are bright green and tender but still hold their shape.

Drain the green beans in the colander with the potatoes. Rinse them under cool water for a few seconds so they stop cooking.

Put the drained tuna into the mixing bowl with the dressing and onions. Break the tuna into large flakes with a fork.

Add the warm potatoes and the green beans to the mixing bowl. Toss gently so the vegetables are coated with dressing without breaking up the potatoes too much.