Fifa said that they will look into the matter and get both sides of the story before slapping anyone with fines. Interesting enough though, Zizou is going to be fined, but Materazzi also will be fined/suspended based on what he said. Nobody knows what was said quite yet, but there have been rumors that Zidane did speak to an official and he said that Materazzi told Zidane that the French team "Are nothing but africain monkeys and that you [Zidane]are just another muslim terrorist"
These are just rumors, but you can remember that Zidane doesn't take lightly on the topic of muslims and terrorists. The media/tabloids did bomb him once saying that his father was part of a terrorist regime and such...
Keep in mind though, these are all rumors just for now and nothing confirmed except the fines by Fifa.