Calais officials said the man was "crushed" by pallets and was found by a Hungarian driver at about 07:00 BST.
The Iraqi man was travelling with two other family members, who were unhurt, a spokesman for the Prefecture du Pas de Calais said.
He is the 12th person to have died trying to cross the English Channel to reach Britain since late June.
Last week, a teenager, thought to be from east Africa, was killed by a freight train near the Channel Tunnel entrance in Calais.
Days earlier a man died when he was electrocuted at the tunnel entrance.
The situation in Calais is part of a wider migrant crisis across Europe, with huge numbers of people heading north from the Mediterranean.
A 20-year-old Iraqi has been found dead in a UK-bound lorry in Calais port, French authorities have said.