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.

Rochdale's Joe Bunney broke the deadlock, netting from six yards before Nathaniel Mendez-Laing doubled the lead against his old club from close range.
Michael Smith then halved Posh's deficit from 25 yards 10 minutes before half time.
Rochdale's Bunney and Posh's Chris Forrester both saw second-half efforts well saved as the Dale held on.
The result ends Peterborough's play-off hopes, with Posh sitting 14 points outside the top six, while Rochdale keep their slim play-off hopes alive, with seven points separating them and the top six.
Rochdale Manager Keith Hill told BBC Radio Manchester:
Media playback is not supported on this device
"We're still chasing the dream, it's a massive dream but the players have stood up to the challenge.
"The recent form is absolutely superb and I'm really pleased with today's performance.
"Our attitude, our grit, our determination in the second half to keep the second half clean sheet was magnificent."
A 20-year-old Iraqi has been found dead in a UK-bound lorry in Calais port, French authorities have said.
[NEXT_CONCEPT]
Peterborough were narrowly beaten by Rochdale as all three goals came in the first half at the ABAX Stadium.