I found a very interesting article based on the differences between movie and the novel. I'll quote some of them, that should answer your question:
Robert Zemeckis, director of Forrest Gump, chooses not to include several adventures that are present in the book and to change the character’s personality.
This significant changes play an important role in the viewer’s perspective of Forrest. Also he is described as a big, tall, and a really strong person while in the movie the viewer would describe him as an average man.
Jenny, and Forrest’s mother are the only two people that love Forrest the way he is. In the book, however, it seems as if Forrest’s mother doesn’t take him more than just an idiot. “How you gonna have a plan, Forrest?..You is a idiot. How is po idiot gonna have a plan?”(220)
In the movie Robert Zemeckis decides to change that and makes her more confident in her son’s mental skills. However, his mental impairment doesn’t seem to bother Jenny, the love of Forrest’s life, who’s feelings toward Forrest evolve differently in the movie compare to the book. The viewer of Forrest Gump doesn’t know her real feelings and might even think that the main character is the person to whom she runs for a comfort and a place to stay until she is strong enough to run away again. This change certainly changes the viewer’s perspective on Jenny’s personality.
So basically, the director chooses a different ending because he changed the character's personality; and in order to maintain consistency in this, it's not just the ending that has been changed, as you read the book you should know better than me: some scenes were added, some of them were cut off. All these changes have been made to make the movie more touching. So I quote the answer to your question:
However, the adjustments to the main heroes’s characters and the addition of several touching moments change the book into a heart breaking movie.
You can read the whole article here. Enjoy.