2. Heat the oil in a 12-inch skillet over medium-high heat. Mix the flour, 1/2 teaspoon salt, and 1/4 teaspoon pepper in a small bowl. In batches, coat the pork in the flour, shaking off the excess, and add to the skillet. Cook, turning once, until browned on both sides, about 4 minutes. Transfer to a plate.
3. Add the butter to the skillet and melt over medium-high heat. Add the shallots and cook, stirring often, until softened, about 1 minute. Stir in the cornichons and capers. Add the wine, bring to a boil, and cook until reduced by half, about 2 minutes. Stir in the vinegar and Dijon.
4. Reduce the heat to low. Return the pork to the skillet and cook, turning often, until the sauce thickens slightly, about 1 minute. Season with salt and pepper and serve hot.