Robert Rooney, 35, admitted the offence and was sentenced to three years in prison at Canterbury Crown Court on Friday.
The Vietnamese, including a 15-year-old girl, were found in October last year at Coquelles, France when officers from the UK Border Force stopped Rooney’s car.
The court was told when he was asked to open the luggage box he told officers he had lost the key.
The court was told when he was asked to open the luggage box he told officers he had lost the key.
The box was part opened by force and the three people discovered crammed inside.
Rooney, from Ireland, was searched and the key to the luggage box was found.
Dan Scully, Border Force regional director, said: “Crammed into a confined space inside the roof box must have been terrifying.
“It is thanks to the vigilance of Border Force officers that they were discovered and that Rooney was caught.
“Border Force officers will continue to work with law enforcement colleagues here and in France to ensure that smugglers face the full consequences of their crimes.”
Deputy director Dave Fairclough, from Immigration Enforcement’s Criminal and Financial Investigation (CFI) team, added: “Rooney deliberately placed three people in an extremely precarious situation.
“He was prepared to turn a blind eye to the obvious risks as long as he was benefiting.
“He has rightly been handed a custodial sentence. The message to the callous criminals engaged in immigration related criminality is clear – you will be caught and the consequences will be severe.”
The three Vietnamese inside the luggage box were handed over to the French authorities.
Last year, 39 Vietnamese nationals died in the back of a lorry as they tried to enter the United Kingdom.
A number of people from both Việt Nam and the UK, have been arrested in connection with incident.