Using a sharp knife or mandoline, slice the fennel as thinly as possible, then soak in ice water to crisp up, about 5 minutes. Strain and dry well.
In a large mixing bowl, whisk together the vinegar, mustard and some salt and pepper, then whisk in the olive oil to create a vinaigrette.
Add the dates, basil, cilantro, mint and chile to the vinaigrette. Then add the orange and grapefruit segments and the fennel; toss well. Divide the salad among 4 serving plates and garnish with the pistachios.