If slicing fennel in advance, toss it with lemon juice to keep it fresh.
Make the vinaigrette: Combine shallot and vinegars in a medium bowl, and let stand 10 minutes so the flavors meld. Season with salt and pepper. Whisking constantly, add oil in a steady stream until mixture is thick and emulsified.
Using a mandoline or very sharp knife, thinly slice fennel; place in a large serving bowl. Add mixed greens and mint. Drizzle with vinaigrette, and toss well to combine. Season with salt and pepper; divide among salad plates, and serve.