The festival will nevertheless be made “real” in 2020, “in a way or another”, they added in a statement.
This is coming after France extended its lockdown measures this week.
The organizers did not elaborate on what the alternatives could be but said they hoped “to communicate promptly”.
The prestigious festival was originally scheduled to take place in the south of France from 12 to 23 May.
When the festival was first postponed, its president, Pierre Lescure, said he was “reasonably optimistic” it would still go ahead this year.
Mr Lescure told Le Figaro newspaper at the time that he believed the peak of the epidemic would be “reached at the end of March and that we will breathe a little better in April”.
But on Monday, French President Emmanuel Macron said the country’s lockdown would be extended until 11 May, and that public events could not be held until mid-July at the earliest.
The film festival, one of the largest in the world, was initially due to take place from May 12-23.
The Cannes Film Festival, until 2003 called the International Film Festival and known in English as the Cannes Film Festival, is an annual film festival held in Cannes, France, which previews new films of all genres, including documentaries from all around the world.
AFP