Place the quartered potatoes in a large pot and cover with cold, salted water. Bring to a boil and cook until fork-tender, about 15-20 minutes. Drain immediately.

While potatoes are still warm, transfer them to a large mixing bowl. In a separate small bowl, whisk together the Dijon mustard, red wine vinegar, and sugar.

Slowly drizzle the olive oil into the vinaigrette while continuously whisking to emulsify slightly. Season generously with salt and pepper.

Pour about half of the dressing over the warm potatoes. Gently toss to coat, allowing the potatoes to absorb the flavor. Add the sliced shallots, chopped cornichons, parsley, and chives.

Add more dressing as needed, tossing carefully to avoid breaking up the potatoes too much. Taste and adjust seasoning—add more salt, pepper, or vinegar if desired.

Allow the salad to rest at room temperature for at least 30 minutes before serving to let the flavors meld. Serve warm or at room temperature.