"The judges have closed their dossier and it was sent to the prosecutor on April 30," he said yesterday.
The prosecutor now has three months to prepare his submissions on whether to dismiss the case or put it forward to court.
In the meantime interested parties can produce written depositions. However if, as is currently the case, there is no defendant's name attached to the proceedings, the case is likely to be dismissed.
Arafat's widow Suha lodged a complaint at a court in Nanterre in 2012, claiming that her husband was assassinated, sparking the inquiry.
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The same year, Arafat's tomb in Ramallah was opened for a few hours allowing three teams of French, Swiss and Russian investigators to collect around 60 samples.
A centre in the Swiss city of Lausanne had tested biological samples taken from Arafat's personal belongings given to his widow after his death in Paris, and found "abnormal levels of polonium", but stopped short of saying that he had been poisoned by the extremely radioactive toxin.
However French experts "maintain that the polonium-210 and lead-210 found in Arafat's grave and in the samples are of an environmental nature," Nanterre prosecutor Catherine Denis said last month.
Polonium-210 became famous in 2006 when a fugitive Russian intelligence officer turned opponent of President Vladimir Putin, Alexander Litvinenko, was killed in London by a strong dose of the hard-to-get radioactive isotope.
The lawyer of Arafat's widow Souha Arafat could not be immediately contacted for comment.