Place potatoes into a large heavy-bottomed pot. Cover with cold water and place over medium heat. Cover the pot and bring to a boil. Immediately reduce heat and remove lid. Gently simmer until potatoes are fork tender. Drain and place into an ice bath to cool. Remove skin by rubbing with a tea towel. Slice potatoes into rounds or cut into large dice and place into a zip top bag. Add the vinegar and toss to coat all of the potatoes. Place the bag into the refrigerator overnight.
In a large mixing bowl, combine the mayonnaise, mustard, parsley, tarragon, garlic, cornichons, onions, and celery. Once evenly combined, add the potatoes and season with salt and pepper. Let the salad chill in the refrigerator for at least an hour before serving.