Unfortunately, there is probably not a better film for 3200 speed. I see you are using Ilford films, you could try HP5+ pushed to 1600, it should respond fairly well, but it might get a little bit contrasty. If you want to use some Kodak, you could also do the same with Tri-X or Tmax 400. Not sure that the grain would be any smaller, it is just what happens. If you have recorded your exposures, you might want to take a look and see if you have enough light for something slower.
I shot some basketball as a stringer for the college paper. I used flash, but I know that it may not be allowed in certain circumstances, so fast film is the answer. With a slower film, you might have to go with slower shutter speeds and have the ball blurred, for instance. If done right, this can add to the effect, but then, it may not be the effect you want. Having said all that, I am not particularly bothered by the grain in this shot. The one thing that I think would have improved this specific image is for you to have aimed higher. More of the goal (backboard) would have been better and less of the floor. The players and the ball would still be there intact.
Shoot basketball low and behind and just to the side of the hoop. I have shot sports professionally off and on for more than 2 decades including NBA games for the AP.