In a medium bowl, gently toss salad ingredients: figs, arugula, olive oil, balsamic vinegar, and shallots. Season with salt and pepper.
Season halibut fillets with salt and pepper. Heat a skillet over medium-high heat; add olive oil. Place halibut in pan and brown on one side, approx. 3 minutes. Flip fillets and transfer to oven; bake for approx. 5 minutes per inch, till cooked through.
While fish cooks, dice peaches and place in a bowl; stir in chutney, set aside.
To serve, place salad mixture on 2 plates, top with halibut filets and garnish with peach chutney sauce.