Omer Guney died from a serious brain illness in Paris's Pitié-Salpiètre hospital on Saturday at the age of 34, sources have told the media.
He was the only suspect to face prosecution for the murders of Sakine Cansiz, 54, a founder member of the Kurdistan Workers Party (PKK) guerrilla group who was close to its leader Abdullan Ocalan, Fidan Dogan, 28, and Leyla Soylemez, 24.
Their bodies were found early on 10 January 2013 at a Kurdish Information Centre in northern Paris with bullet holes in their heads and necks.
Gurney, who was to face trial on 23 January and 10 February 2017, denied killing them, even though investigators said they had CCTV footage of him entering the centre and found one of the victims' DNA on his coat and gunpowder in his bag.
Lawyers Sylvie Boitel, Antoine Comte, Virginie Dusen, Jan Fermon and Jean-Louis Malterre, said the victims' families were furious at being "denied a public trial which they had been waiting for almost four years" and expressed "consternation at seeing France, once again, incapable of judging a political crime committed on French territory by foreign secret services".
Turkish secret service agents implicated
Guney has been described as a Turkish ultranationalist by relatives and was said to have infiltrated the PKK to spy on it.
One source said he was given the task of "eliminating PKK cadres".
French investigators concluded that members of the Turkish secret services, MIT, were implicated in the murders, according to sources, but were unable to establish whether they acted on orders or on their own initiative in order to undermine peace negotiations between the government and the PKK.
The MIT formally denied involvement in January 2014.
The PKK launched an armed campaign for independence in 1984 but has since changed its demands to greater autonomy and more rights for the Kurds, Turkey's largest ethnic minority.
President Recep Tayyip Erdogan's government abandoned peace talks and launched a new anti-PKK offensive in 2015.
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