The men, kidnapped in 2010 while working for French nuclear group Areva and a subsidiary of construction group Vinci in northern Niger, were freed on Tuesday after secret talks.
They men boarded the jet with French Foreign Minister Laurent Fabius and another minister dispatched to collect them.
Thierry Dol, one of the freed men, said: "I am very happy. It was difficult, the ordeal of a lifetime."
Mr Fabius denied the government had paid a ransom, but many French media and analysts, citing anonymous sources, said money had changed hands.
The minister said the men were in shock, having been isolated for so long.
The men's release could benefit President Francois Hollande politically a day after a poll showed he had become the most unpopular French president on record.