Preheat the oven to 425°F.
Place the branzino on a baking sheet, drizzle with olive oil and sprinkle liberally with salt and pepper, including the cavity.
Heat a large ovenproof skillet over high heat. Add the branzino and cook for 3 minutes per side, until the skin is crisp. Transfer to the baking sheet and roast for 10 minutes, until cooked through.
Bring a large pot of salted water to a boil for the green beans. Prepare an ice bath by filling a large bowl with water and ice. When the water boils, add the green beans for 2 to 4 minutes then immediately put them into the ice bath to stop cooking. Take them out of the ice bath after 1 to 2 minutes. Return to the pot
Whisk all of the dill creme fraiche ingredients together in a large bowl. Add the green beans, radishes, and fennel and toss to coat.
To serve, divide the salad between plates. Top with branzino and a lemon wedge.