Purchase a baby's hair brush that you'll use to remove the cat fur. It should have extremely soft bristles that won't damage the surface of the sofa.
Brush the couch going with, not against, the direction of the nap. You should notice the fibers lying down in a single uniform direction. In most cases, the nap runs toward the front edge of the sofa on seat cushions and downward on the sides and seat backs.
Use a vacuum that has a suction hose to gently remove stubborn cat fur that did not fall during the brushing. Since velvet is delicate, it's important to test your vacuum hose on an obscure area first to make sure the suction strength isn't strong enough to damage your couch.
Run the baby's hair brush over the surfaces of the sofa one last time to remove any strays. This method should leave your surface fur and dust free.