Heat a small skillet over high heat. Add the andouille and cook, stirring, until sizzling, about 1 minute. Transfer to a medium bowl and let cool to room temperature. Mix the sausage with the sliced olives, softened butter and minced shallot.
Light a grill. Rub the salmon fillets all over with olive oil and season lightly with salt and pepper. Grill the salmon over high heat, turning once, until nicely charred and just cooked through, about 3 minutes per side. Transfer the salmon to plates, top with the buttered andouille mixture and serve immediately.