Preheat oven to 350 degrees.
In a small pot, combine vinegar, sugar and 1/4 teaspoon sea salt. Heat until salt and sugar are dissolved. Add sliced radishes to a small jar. Pour liquid over radishes and let sit until cool.
Cut the fennel bulb into slices and place in a baking dish. Drizzle with 1 tablespoon olive oil and toss until evenly coated. Bake in oven for 20 minutes until tender and golden in color.
While fennel is baking, bring a pot of water to a boil. Cook green beans for 3 minutes, until slightly tender; then drain and rinse with cold water to stop them cooking further.
In a food processor, combine lemon juice, capers and olive oil. Blend until capers are roughly chopped. Season with sea salt and pepper, to taste.
In a salad bowl, combine green beans, fennel and pickled radish. Drizzle with dressing and toss well to combine.