It's basically cooked potato slices tossed with vinaigrette while still warm.
I haven't followed a recipe in years, as it's pretty simple.
Most recipes would have you cook the potatoes whole and peel and slice them while still hot. Julia has an easier method, below.
Either way, toss the warm potatoes with a splash of white vermouth, a dash of vinegar, and a dribble of the potato-cooking water. Add a minced shallot, season with salt and pepper, and toss the potatoes a few times while they cool and absorb the liquid. (You may need to add more.) When lukewarm, fold in some chopped parsley and some olive oil. Taste for seasoning. Enjoy warm or cold. That's all there is to it. I've never used tarragon but I may have to try it.
Here's Julia's potato method:
Cut "boiling" potatoes in 1/4-inch thick slices. Add to cold salted water and bring just to the simmer. Cook gently, without boiling, until just tender. Bite into a few slices to check. Save some of the water for the salad, then drain the potatoes. Return them to the hot pan and cover it. Let them sit for 4 minutes to firm them up (This is important!) Turn out into a large bowl and dress them while still warm.
This works for American-style potato salad too. Toss the warm potatoes with cider vinegar and the potato water. When cool, add all your favorite "stuff" along with your mayonnaise dressing. The potatoes are really moist this way and don't drink up so much mayo.