Cardiff announced the club record signing of Sala in January for £15m but the Argentine never got to play for the club as he died in a tragic plane crash two days after the deal was struck.
Sala was flying from France to England, alongside pilot David Ibbotson, to join up with his new team, when their Piper Malibu N264DB plane crashed into the sea along the English channel.
The light plane was found 67 metres underwater in February, 21 miles off the coast of Guernsey in the Channel with the search party retrieving Sala’s body from it but that of pilot Ibbotson has never been found.
Cardiff City, who have since been relegated from the Premier League, opted against paying the agreed first installment of the transfer fee because they insist Sala’s registration was incomplete before he died.
Nantes lodged a complaint with FIFA Players’ Status Committee, who have ruled in favour of the French club.
A declaration from world football's governing body said: "In a meeting held on 25 September 2019 the FIFA Players' Status Committee established that Cardiff City FC must pay FC Nantes the sum of EUR 6,000,000, corresponding to the first instalment due in accordance with the transfer agreement concluded between the parties on 19 January 2019 for the transfer of the late Emiliano Sala from FC Nantes to Cardiff City FC.
"The FIFA Players' Status Committee, which never lost sight of the specific and unique circumstances of this tragic situation during its deliberations on the dispute at stake, refrained from imposing procedural costs on the parties.
"The findings of the decision were notified to the parties concerned today.
"Within a deadline of 10 days, Cardiff City FC and FC Nantes can request a copy of the grounds of the decision, which can be appealed to the Court of Arbitration for Sport in Lausanne."