Preheat oven to 200° and put a roasting pan half full of water on the bottom rack. Oil a rimmed baking tray and arrange salmon on one side. Pile fennel on other side and drizzle both with olive oil, then sprinkle both with salt and pepper. Toss fennel a little to coat and spread out in pan.
Roast salmon until just firm to the touch, about 30 minutes; let cool. Remove salmon skin and break each fillet into 3 or 4 chunks.
Put fennel in a medium bowl and mix with purslane, olives, and lemon juice and zest.
Arrange salmon on plates with salad and drizzle with a little more oil.