British police said that the body retrieved from the wreckage had been formally identified as Sala.
But strong currents and winter weather forced them to call off the search before locating 59-year-old pilot David Ibbotson - the only other person on the Piper Malibu propeller aircraft.
The Air Accidents Investigations Branch (AAIB) said the search and rescue operation had been carried out "as dignified a way as possible" and the men's families were kept updated throughout.
Sala's body was recovered from the wreckage on the seabed but Ibbotson's body has not been found.
Cardiff, away to Southampton on Saturday, had been given permission by the Premier League to wear shirts embroidered with a yellow daffodil, the national emblem of Wales and the team colour of Nantes.
"We again are sending our serious sincerest sympathies to his family, to Cardiff City to Nantes and to all his fans".
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Sala, who had spent four seasons at Nantes, was travelling to his new club Cardiff City with pilot David Ibbotson, when their plane went missing over the English channel on 21 January.
The French club, which has demanded full payment for the transfer, played their first game since Sala's body was identified with thousands of fans joining his former teammates in a minute's applause before kick-off.
Afterwards, Cardiff manager Neil Warnock dedicated the win to Sala: "We wanted to do it for Emiliano and I'm really proud the lads have done him justice".
Thousands of tributes to Emiliano Sala at Cardiff City stadium are set to be made into a permanent shrine to the Argentine striker at the home of the Bluebirds.
A statement from the club said the behaviour would not be tolerated and that the two fans would likely be banned as a result.