The Hungarian-born financier was fined $2.8 million in December 2002 - matching the amount he was accused of having made from buying and selling shares of French bank Societe Generale with insider knowledge 17 years ago.
Soros said in 2002 that he was "astounded and dismayed" by the ruling and vowed to appeal "to the highest level necessary". He denied having had inside information and called the charges against him "unfounded and without merit".
Soros, 74, did not speak to reporters as he walked into court on Thursday with lawyers. The appeal court's decision is not expected for weeks.
During his trial, he said: "I have been in business all my life, and I think I know what is insider trading and what isn't."
Societe Generale was privatised in 1987. A year later, its stock price went up during an unsuccessful takeover bid. Soros was accused of having obtained insider information before the abortive corporate raid pushed up the stock price.
French stock market regulators first noticed anomalies in the Societe Generale stock surge in 1989. Soros was put under judicial investigation - one step short of being charged - in June 1993 but the trial was delayed until 2002.
"I have been in business all my life, and I think I know what is insider trading and what isn't"
Prosecutors said the case dragged on because Swiss authorities took years to respond to requests for information.
Defence lawyers had argued the case should be thrown out because it took so long to bring to court.
Soros said he was interested in Societe Generale based on information he claims was widely known: France's leftist government of the time favoured takeovers to change the leadership at recently privatised companies.
Soros said he was buying stock in many companies and had no reason not to include Societe Generale. Afterwards, he sold the stock, saying he felt the takeover attempt was politically motivated and was not going to benefit the company.