Place the potatoes in a large pot and fill with cold water to 1-inch above the potatoes. Season the water with 1 tablespoon salt. Bring to a simmer and cook until a knife gently plunges through the potatoes, about 15 minutes. Reserve 1/3 cup of the cooking water, drain the potatoes and put back into the pot (off the heat) to keep warm.
Meanwhile, fry the bacon in a skillet over medium heat until crispy, stirring occasionally. Reserve the bacon and drain all but 1/4 cup bacon fat. Add the onions and saute until slightly golden. Add the vinegar and, with a wooden spoon, scrape up any bits from the bottom of the skillet. Add in the reserved cooking water and reduce until it thickens, about 3 minutes. Off the heat, whisk in the mustard and season with salt and pepper. Add in the potatoes, bacon and tarragon and toss to combine. Adjust the seasoning if necessary.