The lawyers said FIFA's Football Tribunal had ruled that Cardiff "must pay" just over 11 million euros (£9.45m) corresponding to the last two instalments of the 17m-euro fee agreed between the two clubs.
Cardiff will also have to pay interest on the fee and $25,000 in procedural costs, according to the decision, obtained by AFP.
Sala, a former Argentine striker, died when the light aircraft taking him to the Welsh capital came down in the Channel on January 21, 2019, two days after he had signed for the then Premier League side.
"FC Nantes is delighted with this latest victory before FIFA. The club's rights have been confirmed. It hopes that, after four years of proceedings, Cardiff City FC will finally respect its financial commitments and stop its relentless litigation", lawyers Jerome Marsaudon and Louis-Marie Absil told AFP.
They said Nantes "is looking forward to bringing the legal aspect of this tragic accident to a definitive close".
Cardiff paid a first instalment of around 6 million euros last January, after an initial decision against it by world football's governing body followed by an unsuccessful appeal to the Court of Arbitration for Sport.
Nantes diced with relegation from Ligue 1 last season and only escaped the bottom four on the final day in May.
Cardiff were relegated from the Premier League in 2019. The club have insisted for the past four years that Sala's transfer had not been finalised at the time of his accident.
In May they launched a counter-claim in France for around 100 million euros. The Nantes Commercial Court said last week it would hold a hearing on the merits of that case, probably in the second quarter of 2024.