Bring a large pot of salted water to a boil. Add the green beans, cook until just tender, 3 to 5 minutes, and drain.
Meanwhile, in a large bowl, combine the lime juice, vinegar, cayenne pepper, tarragon, and 1/4 teaspoon salt. Whisking constantly, slowly add the oil in a thin, steady stream until emulsified.
Add the beans to the vinaigrette and toss. Serve warm or at room temperature.