British fashion designer John Galliano, who has admitted anti-Semitic insults at a Paris restaurant, has been given suspended fines totalling 6,000 euros (£5,250; $8,400).
The designer, fired by the Dior fashion house over the affair, said he had no recollection of the two events and denied being racist.
Galliano apologised for his behaviour at a one-day trial in June.
He blamed drug and alcohol addictions for his outburst.
The BBC's Christian Fraser, in Paris, says the greatest punishment has been the damage to Galliano's career; he was sacked by Dior after his arrest and the cost to his reputation has been far bigger than any fine a court can impose.
Our correspondent says the judges were convinced that this was a man who needed help rather than punishment.
A lawyer for Galliano said after the ruling: "Mr Galliano is relieved. Relieved that these eight months are behind him. He is looking forward to a future with understanding and forgiveness, hopefully, and to put all of this behind him."
Galliano did not attend Thursday's sentencing.
In addition to the suspended fines, Galliano was ordered to pay a symbolic euro in damages to each of his victims and to five anti-racism groups who were also complainants. He will also pay legal costs for the plaintiffs.
Galliano had been charged with "public insults based on origin, religious affiliation, race or ethnicity". The offences carried a maximum sentence of six months in jail, but prosecutors did not ask for the designer to be sent to prison.
The fines related to incidents on the evenings of 8 October 2010 and 24 February 2011 at La Perle cafe in the Marais district of Paris.
During his trial on 22 June, the court heard how Galliano harangued museum curator Geraldine Bloch about being Jewish, in the February incident.
He also hurled racist insults at her friend, who is of South Asian origin, for 45 minutes before police came to break up the argument, the court heard.
In a third incident, prosecutors also showed the court an amateur video of Galliano, while drunk, declaring a love for Hitler.
The designer, 50, did not have to enter a plea to the charges at the hearing, but gave mitigating statements to the court about the incident.
He told the court: "They are not views that I hold or believe in. I apologise for the sadness this whole affair has caused."
Galliano blamed mounting pressure at work and said he had developed a crippling addiction to alcohol, Valium and sleeping pills.
So common were these drinking binges his chauffeur was "trained" to telephone a lawyer if the rows became too heated, the court was told.
Galliano says he has undertaken treatment for his addictions.
Galliano took over the creative helm of Dior in 1996 and won British Fashion Designer of the Year on four occasions.