'The families of Mr Sala and pilot David Ibbotson have been updated.
"We offer our most heartfelt sympathies and condolences to the family of Emiliano", the statement said. "He and David will forever remain in our thoughts", the team said on its website.
The footballing world has taken to social media to share their own messages after the tragic news broke. "Our condolences to his family and loved ones".
Although his time at Bordeaux demanded patience - Sala only made 11 league appearances for the club over three years - loan periods at Orleans, Niort and Caen gave him a platform to demonstrate his abilities. "You'll live on forever in our hearts".
That tally also matched his statistics for each of the last two campaigns, and only a certain Lionel Messi has scored more goals this season among Argentine players in the big five European leagues.
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And Arsenal's Mehmet Ozil tweeted: "No words to describe how sad this is".
It was a story typical of the January transfer window - a buying club tenaciously chasing mid-season reinforcements but facing stubbornness from a selling club determined not to be left in the lurch by the loss of one of their key players.
Portuguese club FC Porto's official Twitter account shared a picture of Sala with the caption: "RIP Emiliano Sala". Thoughts and prayers go out to his family and also to the family of the pilot.
Independiente, the Argentine club Sala supported since he was a boy, shared a picture of Sala with the caption: "So long, Emiliano. Finally, now they can get the closure that their hearts must have been yearning for". "It's over; the only thing I hope now is that they find them".
Cardiff and Nantes agreed a £15 million fee for Sala on January 19 and the Argentinian striker's International Transfer Certificate was registered with the FA of Wales two days...
The plane had been cruising at 5,000 feet (1,525 m) when the pilot requested to descend to a lower altitude on passing Guernsey.