In a small bowl, mix onion, 1 tablespoon vinegar, and 1 1/2 cups cold water; let stand at least 20 minutes.
Rinse beans and cut into julienne strips with a food processor, French bean cutter (slicing bars in the handle of some vegetable peelers), or knife. In a 3- to 4-quart pan over high heat, bring 2 quarts water to a boil. Add beans and cook just until tender-crisp, 2 to 5 minutes. Drain beans and immerse them at once in ice water until they are cold. Drain well.
Meanwhile, cut jicama into 1/4-inch-thick sticks.
In a large bowl, mix remaining vinegar with oil, mustard, and oregano. Drain onion. Add onion, beans, jicama, and watercress to bowl. Mix well and add salt and pepper to taste.