Whisk the vinegar, mustard, salt and pepper in a small bowl. Continue whisking and slowly add the oil, in a thin stream. Once the dressing has emulsified, set aside.

If the fennel is very fresh, the surface will be smooth and appetizing; if not, use a peeler to strip off the discolored outer layer. Cut the fennel bulbs in half lengthwise and pare out the tough core. Slice thinly across the grain. Cut the onion in quarters lengthwise and then slice thinly across the grain. Combine the fennel, onion and fennel fronds in a medium bowl. Whisk the dressing once more to re-emulsify if necessary, add to the vegetables, and toss well. Serve at once.