Saad al-Hilli died with his wife and mother-in-law in a shooting in Annecy, France in September. Their killer has not been caught.
"As of today, the chief prosecutor, Eric Maillaud, has found nothing of note," the BBC's Christian Fraser told the Today programme.
Maillaud indicated that the investigation will look "at all mentally unbalanced people [and] everyone connected with the world of guns".
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