Preheat broiler with oven rack about 4 in. from heat.
Snap off bottom of an asparagus spear to see where it breaks easily. Line up remaining spears and slice off bottoms at the same spot. Put trimmed asparagus on a 12- by 17-in. rimmed baking sheet, sprinkle with oil and 1/4 tsp. each salt and pepper, and toss to coat. Arrange asparagus in a single layer on baking sheet.
Season salmon with remaining 1/2 tsp. salt and 1/4 tsp. pepper, then set on top of asparagus in a single layer.
Broil salmon and asparagus until salmon is no longer translucent but still moist in center and asparagus is browned in spots, 8 to 12 minutes. If asparagus isn't done, lift salmon to a platter and return asparagus to oven for a few more minutes.
Meanwhile, whisk together crème fraîche, mustard, chives, and salt and pepper to taste in a small bowl.
Serve salmon and asparagus with crème fraîche sauce.