Place potatoes in a medium saucepan and add cold water to cover by 1″. Bring to a boil, season with salt, and cook until fork-tender, 15–20 minutes. Transfer potatoes to a plate with a slotted spoon. Return water to a boil and cook haricots verts in same saucepan until crisp-tender, about 2 minutes. Using a slotted spoon, transfer to a bowl of ice water. Chill until cold, about 3 minutes. Transfer to paper towels and pat dry. Return water in pot to a boil and cook eggs 8 minutes. Transfer eggs to bowl o...