They said the driver, who was also from Pakistan, was detained.
The discovery came after 39 people, all believed to be Vietnamese nationals, were found dead in a refrigerated truck in Britain last month, laying bare again the risks of illegal migrant routes to Europe.
The group of 31 Pakistani migrants was discovered during a routine check on a motorway near the Italian border on Friday, French prosecutors said.
The migrants, who included three teenagers, were handed over to the Italian authorities in accordance with immigration procedures.
"We will try and establish if we can trace it back to a network and backers as we always do in this type of case," the prosecutors' office in the southeastern city of Nice said.
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