For the sauce, heat the butter, add the flour and sauté while stirring. Deglaze with the broth and the white wine, stirring constantly to create a creamy sauce. Add the crème fraîche and the mustard and season the sauce with salt, pepper, sugar and 1 tablespoon of white wine vinegar.
For the poached eggs, bring about 2 liters of water (approximately 8 1/2 cups) to a boil along with 4 tablespoons of vinegar. Carefully break the eggs into a ladle and slowly slide them into the vinegar water. When the eggs are set, lift from the water with a skimmer and drain.
Transfer to plates and serve drizzled with the mustard sauce and showered with chives.