Bruce MacFarlane, a prosecutor, said Monday's trial had nothing to do with whether Hartmann was a journalist or a former employee, and everything with the fact that she "deliberately published" classified information.
Karim Khan, Hartmann's lawyer, said the judges themselves had made the decisions public by referring to them in later judgments made in open court and therefore there could have been no breach of confidentiality.
Hartmann covered the Balkan wars of the 1990s as a journalist for Le Monde, the French newspaper, and went on to become the spokeswoman for Carla Del Ponte, the former ICTY chief prosecutor, from 2000 to 2006.
After leaving employment with the court, she published the book Peace and Punishment: The Secret Wars of Politics and International Justice, and wrote several articles on the court's work.
Khan said that six months before the book's release, the New York Times and the International Herald Tribune had published articles citing the same facts, without any reaction from the tribunal.
'Insult to victims'
About two dozen Hartmann supporters from the northern French city of Lille protested outside the court, waving a banner reading: "Sentences for war criminals, not journalists".
A support committee had sent Patrick Robinson, the ICTY president, a petition containing more than 3,500 signatures of people demanding Hartmann's acquittal.
Nanou Rousseau, the president of lobby group Mothers for Peace, which supports the journalist, said: "Florence Hartmann was only doing her job as a journalist.
"This trial should not be happening. It is an insult to the history and the victims who are denied the right to know the truth."
More than a dozen people have been prosecuted for contempt of the ICTY. Four journalists have been fined, including one who was also jailed for three months.
Other people have been prosecuted for witness intimidation.
The trial is set to continue until Wednesday.