Cut potatoes into 1/8-inch thick slices, using a mandoline or a sharp knife. Place sliced potatoes in cold water until ready to use. Make certain not to soak the potatoes too long, as they will lose their starch. Drain before use.
Heat 1 tablespoon oil in a large sauté pan over high heat. Add shallots and garlic and sauté until glossy. Add potatoes and sauté 2 minutes. Add vinegar and 1/8 cup cold water and reduce heat to medium. Simmer until potatoes are crisp tender and the liquid is syrupy, 8 to 10 minutes. Stir in mustard, sugar, fennel greens, chives and remaining oil. Season to taste with salt and pepper.
Place potatoes in the center of each serving plate. Top with herring and a dollop of herbed double crème. Garnish with spring greens and a drizzle of chive oil.
For the Herbed Double Crème:
In a large bowl, stir together double crème, vinegar, dill, parsley, thyme, shallots, and garlic until well combined. Season to taste with salt and pepper.
For the Chive Oil:
Place the chives and oil in a food processor or blender and process until well combined. Pour the oil into a fine-nozzled squeeze bottle and store refrigerated for up to 2 weeks.