By Abdoulaye Massalatchi and Nicholas Vinocur
NIAMEY/PARIS (Reuters) - Four Frenchmen held hostage in the Sahara desert by al Qaeda-linked gunmen for three years flew home and were reunited with their families on Wednesday, with Paris dismissing media reports it had paid a ransom for their release.
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 negotiations conducted by the government of Niger.
"I am very happy. It was difficult, the ordeal of a lifetime," said Thierry Dol, one of the freed men before leaving.
Gaunt and bearded, but said to be in good health, the men embraced their families on the runway of a military airport near Paris where President Francois Hollande was waiting.
Media reports, citing unnamed sources, that a 20 million euro ($27.5 million) ransom had been paid by France's external intelligence service overshadowed their homecoming, but the government said Hollande has banned paying hostage-takers.
"I want to hail their courage after three years of struggle, of waiting, of suffering," Hollande said. "Today our four friends are back with their friends and family, and I wish them everything that free men could want."
Pierre Legrand, Daniel Larribe, Thierry Dol and Marc Feret, wearing sun glasses and scarves, hugged relatives and shook hands with ministers, but declined to talk to waiting reporters.
Foreign Minister Laurent Fabius, who travelled back with them to France, said the men were in shock, having been isolated for so long. "They slept well, but on the floor as they are not yet able to sleep on mattresses," he said.
Niger's President Mohamadou Issoufou said they had been retrieved from a remote area of northern Mali after Niger officials made contact with the kidnappers a few months ago.
"We always remained confident because we had regular contacts," Issoufou told Le Figaro newspaper.
Sources said negotiations with the hostage-takers were led by Mohamed Akotey, a Tuareg who joined Areva's staff after the end of a rebellion by the Niger Movement for Justice.
Fabius and government spokeswoman Najat Vallaud-Belkacem both said France had stuck to its policy of not paying ransom.
However, Diane Lazarevic, daughter of one of seven remaining French hostages abroad, told Europe 1 radio the foreign ministry had told her that while the government would not pay the kidnappers, their employer might do so.
Areva declined to comment and the ministry was not immediately available to respond to Lazarevic's account.
The ransom allegations dominated French media coverage and may limit any political benefit for Hollande, a day after a poll showed him to be the most unpopular president on record.
Earlier this year, after ordering French military intervention in Mali to prevent al Qaeda-affiliated Islamists taking over the country, Hollande announced that France would no longer pay ransom to release hostages.
Shortly afterwards, diplomats said Hollande agreed to a British initiative to enshrine a commitment not to pay ransom to "terrorists" in the communiqué of the Group of Eight leaders' summit in Loch Earn, Northern Ireland, in June.
Britain says it is less vulnerable to hostage taking because of its credible refusal to pay. Critics say this had led to British hostages being killed by their captors.
France has not gone as far as Britain by outlawing ransom payments by companies.
Nigerian Islamist sect Boko Haram was paid an equivalent of $3.15 million by French and Cameroonian negotiators before freeing seven French hostages in April, a confidential Nigerian government report seen by Reuters showed.
Western and regional security officials say kidnapping has earned al Qaeda in the Maghreb (AQIM) tens of millions of dollars, although no figures have been confirmed. The money has allowed the group to buy food, fuel, weapons and favor among local populations in remote zones of Mali's north.
Insurgents in Mali have threatened reprisals against French targets. AQIM said in March it had beheaded one hostage and could kill the others. The Frenchman's body was found in July.
Of the seven French citizens still captive abroad, four are in Syria, two in the Sahel, and one in Nigeria.
($1 = 0.7262 euros)
(Additional reporting by Emmanuel Jarry, Ingrid Melander and Paul Taylor in Paris; Writing by David Lewis and Ingrid Melander; Editing by Alistair Lyon and Andrew Heavens)