Cook potatoes in a pot of boiling salted water until tender, about 20 minutes. Drain well. Cool slightly.
Place greens in a large bowl. Add potatoes.
In a small bowl, whisk together red-wine vinegar, mustard, honey and salt. Whisk in olive oil. Stir in tarragon.
Just before serving, fill a deep skillet with water, bring to a boil and add vinegar. Break eggs into a bowl and slip into water, one at a time. Cook for 3 or 4 minutes, or until whites are set and yolks are still liquid. Lift eggs out of water with a slotted spoon and drain on paper towels. Trim off any scraggly edges.
Toss salad and potatoes with dressing. Divide among four plates. Top each serving with two slices of smoked salmon and one or two eggs. Serve immediately.