The Welsh club took the case to the Nantes commercial court in 2023 for loss of income and other damages suffered by Cardiff as a result of the player's death.
Monday's ruling ordered Cardiff to pay Nantes 300,000 euros (£261k) in moral damages suffered by the French club.
Sala, a 28-year-old forward, died when the light aircraft taking him to the Welsh capital came down in the English Channel on January 21st, 2019, two days after he had signed for the then-Premier League side.
He and pilot David Ibbotson were killed.
Following an analysis conducted by an expert appointed by Cardiff City, the club estimated their losses at 122 million euros.
Since Sala's death, Cardiff have been relegated from the Premier League. They currently play in English football's third tier.
"We initiated this process so that the full truth would come to light in this case and out of respect for the memory of Emiliano Sala," Cardiff's lawyer Celine Jones told reporters after the verdict.
"Today, we bitterly observe that the principles of transparency, integrity, and safety in professional football have not prevailed in this decision," she added.
Sala's mother, Mercedes Taffarel, was in court with Cardiff representatives but did not wish to speak.
Nantes, struggling in the Ligue 1 relegation zone this season, welcomed the decision.
"Nantes are in no way responsible for the incident that occurred," said club lawyer Jerome Marsaudon said.
"We are pleased the court listened to us and confirmed this in clear terms."
During their pleadings, lawyers for Nantes denounced the "judicial harassment" by Cardiff, accusing the club of having "exploited" the death of Sala.
Louis-Marie Absil, counsel for Nantes, said the total sum sought by Cardiff in damages was "totally fanciful and exaggerated".
'Can never happen again'
Cardiff argued Nantes, through their intermediary, agent Willie McKay, were the organisers of the private flight on which the footballer was travelling and that, if the transfer was effective at the time of the accident according to the Court of Arbitration for Sport (CAS), it is the organisation of this flight that was at issue.
CAS ruled in 2022 that Sala's transfer had definitely been finalised at the time of his death.
The following year, world football's governing body FIFA ordered Cardiff to pay Nantes the balance of Sala's transfer fee, which at the time amounted to just over 11 million euros out of a total of 17 million euros.
A statement issued by Cardiff on Monday read: "We deeply regret that the court did not recognise FC Nantes' liability in this tragedy.
"How is it possible that, in the end, FC Nantes - which never contributed to the support fund we launched in memory of Emiliano - paid more money to Willie McKay (1.5 million euros) than to the Sala family?
"More than ever, there is an urgent need to strengthen safety and ethical standards in the management and protection of players, so that such a tragedy can never happen again.
"The world of football must take a hard look at itself."