In the Way Back Machine: Tall Story
I saw it when it was released in 1960, starring Anthony Perkins. It had earlier been a successful play and the movie was directed by Joshua Logan of Sayonara and South Pacific fame..
If Anthony Perkins doesn't strike you as a basketball star, consider that the leading lady was the first movie role for Jane Fonda -- definitely counter the roles she later played. Also, I just read, Robert Redford played a bit part as a member of the hoops team -- definitely the first movie role for him.