In a small pot on the stove, or in a small bowl in the microwave, warm 2 tablespoons water until hot. Remove water from the heat, add the saffron, and let infuse until the water turns bright yellow, about 10 minutes. Strain through a fine-mesh sieve, discard the saffron threads, and set the liquid aside.
Whisk together the olive oil, lime zest and juice, vinegar, mint leaves, and saffron water. Season the vinaigrette with salt and pepper, to taste. In a salad bowl, toss the fennel, apricots, and tomatoes together with the vinaigrette and season with salt and pepper, to taste.