This salad is made not with haricots verts but with regular green beans, which should, of course, be tender and fresh. Chef Eberhard Müller, in the German tradition, adds a pinch of sugar to his vinaigrette to make it a little less harsh; judge for yourself. If you have a mandoline, use it to slice the fennel thinly and evenly.
Cook the beans in a large saucepan of boiling salted water until nearly tender, about 6 minutes. Drain them in a colander and refresh under cold running water. Drain well.
In a medium bowl, combine the olive oil and lemon juice and season with salt and pepper. Thinly slice the fennel lengthwise, add it to the bowl and toss, then transfer the fennel to a platter. Add the beans to the bowl and toss with the remaining dressing, then transfer them to the platter. Garnish with the Parmesan shavings and serve.