The four freed Frenchmen were captured in September 2010 by the North African wing of al-Qaida and spirited from their dormitories in the town of Arlit, Niger, where Areva, a French state-run nuclear company, operates a uranium mine.
Officials had long suspected the hostages were being held in northern Mali, a harsh desert area where there is no tree cover and the blazing midday heat can soar to 40 degrees Celsius (104 Fahrenheit). Previous hostages have recounted being bitten by scorpions.
The question of whether ransom was paid to procure their release immediately rose to the fore.
Hollande had made clear his government would not pay ransoms to free French captives. That sparked an outcry from families of French captives in West Africa, where hostage-taking has been a lucrative business for radicals. Fear was redoubled when in January France invaded Mali as part of an anti-terror offensive.
Pascal Lupart, who, as the head of an association representing friends and families of the hostages, is in touch with those investigating the case, said he was told Areva paid a ransom for the captives. He did not know the amount, however, and an Areva press officer, Julien Duperray, refused to comment on the claim.
Former French Defense Minister Gerard Longuet also downplayed the notion held by many who have observed the case that Areva would pay a ransom in lieu of a direct payment by the government. "One cannot imagine that a state company would do the contrary" and pay to free the men, Longuet said on BFM-TV.
Global intelligence company Stratfor estimates that al-Qaida in the Islamic Maghreb, or AQIM, has carried out at least 18 kidnappings since 2003, raising an estimated $89 million in ransom payments.
AQIM began as an Islamist insurgency in Algeria and became an official chapter of al-Qaida in 2006. It moved into northern Mali and prowled the vast terrain of other countries in the Sahel region, including Niger, in search of captives.
An analysis of AQIM's past kidnappings shows that the organization got better with each passing year at extracting money from Western nations and businesses, shooting up from an estimated $400,000 per hostage in 2003 to roughly $3 million per hostage in July 2012, according to a Stratfor report.
Analysts say France is one country that has previously paid substantial ransoms to free its citizens though the French government has always denied it. "We don't play that game," Le Drian, the French defense minister, told TF1 television from Niamey.
France intervened in Mali at the start of the year to push out Islamic extremist fighters in the north. That operation may have undercut the desire to pay ransoms because the hostage takers could have used the funds to buy arms and train fighters to battle French soldiers. Some 3,000 French troops remain in Mali.
Although military experts say several hundred fighters were killed and AQIM was flushed out of much of northern Mali as a result of the French-led operation, there is evidence that the jihadists have simply sought refuge across the vast desert border in southern Libya, Algeria and parts of Tunisia.
The French president, who announced the release of the captives during a trip to Slovakia, said France's efforts to free hostages in Africa had been interrupted by the invasion, but resumed as soon as feasible.
Hollande thanked his Niger counterpart, Issoufou, who, in his appearance with the freed Frenchmen, offered a string of congratulations, including to "members of the Niger team" an apparent reference to those who took part in procuring the hostages' freedom.
"I congratulate the hostages and their families who are now going to be able to hug them after several years of detention," Issoufou added.
Areva chief executive Luc Oursel said in a statement: "This liberation is an immense joy for the families and for all Areva employees. The men showed extraordinary courage."
Rene Robert, the grandfather of Legrand, said, "What we lived through for three years I hope that no one else has to live through."
There have been tragic endings for some French taken hostage. Philippe Verdon, who was kidnapped in western Africa in 2011 in an attack claimed by AQIM, was found dead in Mali this year, with a shot to the head.
At least seven French are still held hostage in other countries: two in the Sahel region, where Mali and Niger are located; one in Nigeria; and four in Syria.
Hollande sent a message to those still in captivity, saying that today's good news means they should "never give up hope."
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Sarah DiLorenzo in Paris, Krista Larson in Dakar, Senegal and Dalatou Mamane in Niamey, Niger, contributed to this report.
