But lawyers for his widow, Suha Arafat, have argued that his death was a political assassination and vow to appeal the decision in court.
"The lack of investigation leads inevitably to the conclusion that there is insufficient evidence," the lawyers said, calling for more experts to be questioned.
Arafat died in Percy military hospital near Paris aged 75 in November 2004 after developing stomach pains while at his headquarters in the West Bank city of Ramallah.
Arafat`s body exhumed in 2012
An investigation was opened in August 2012 at the request of his widow and his remains were exhumed and examined separately by French, Russian and Swiss experts.
A laboratory in the Swiss city of Lausanne had tested biological samples taken from Arafat`s belongings that were given to his widow after his death, and found "abnormal levels of polonium." But it stopped short of saying that he had been poisoned.
French experts found that the isotopes polonium-210 and lead-210, found in Arafat`s grave and in the samples, were of "an environmental nature," Nanterre prosecutor Catherine Denis concluded in April.
The head of the Palestinian Authority`s inquiry committee on Wednesday refused to accept the judges` conclusions, but has yet to offer its own findings. Some people in the Palestinian Territories blame Israel for Arafat`s death.
"We`ll continue our investigation to reach the killer of Arafat, until we know how Arafat was killed," Tawfiq Tirawi told the AFP news agency.
The official cause of Arafat`s death was a massive stroke, but French doctors were unable at the time to determine the origin of the illness and there was no autopsy.
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