If we consider a free falling body and the Earth as the system, then the gravity is an internal force and there are no other external forces acting on the body. Then how do we explain the displacement of the centre of mass of the body as we know only external forces can displace the centre of mass ?
When a body moves towards earth due to gravitational force, an equal amount of force acts on earth too which causes not only the body to move towards the earth but also the earth towards the body but with negligible speed (because of negligible mass of body as compared to earth). All this happens such that the centre of mass of earth-body system doesnt get displaced because no external force acts on the system . So, basically, the center of mass remains undisplaced because both the body and earth move towards each other because of their gravitational force (internal force).