Only when he stops falling (i.e., when he hits the floor). A little earlier, if the planet has atmosphera.
An astronaut as you describe it is in free fall. All of the particles in his body feel the same acceleration, so he has no way of sensing which it has acceleration (when you stand on the ground, your feet feel the force on the ground needed to annulate acceleration due to gravity, which is what you are actually feeling).
Even if the speed becomes so big to begin having relativistic effects, for him everybody will be normal (if he had a watch that he could test by touch, he would not feel any time dilation/contraction).
Once he enters an atmosphera, he will begin sensing friction. Of course, that will not mean that he will know where down is, because friction will just mean a deceleration is applied with the direction opposite of his velocity. If he is facing in the direction of his movement, he will feel some force pushing his front body back.
If the direction of movement becomes down, he will feel that such forces increases progresively, as the atmosphera becomes denser and denser. He may feel the heat, too.
Of course, once he reaches the ground, what remains of him cannot continue advancing. The impact at terminal speed should give a good indication of what the direction of gravity is; and after all, each reamining chunk of astronaut (if any) feels the force the ground applies on it to compensate to gravity (since he is subject to gravity and does not move, the ground is exerting the force needed to compensate gravity).
If the planet has no atmosphera, the first hint of the action of gravity would be act of landing (and cratering) such planet.