Police said they have little information about the identity of the suspect who killed Saad al-Hilli, his wife, Iqbal, her mother, Suhaila, and a passing cyclist, Sylvain Mollier, last year.
"We don't know who they are except that they could hit a moving target and change cartridges. It is clear this was a hardened gunman," police told The Guardian.
The investigation has led French detectives to Iraq, where al-Hilli was born, as well as Switzerland, The Guardian said.
Police said al-Hilli had an unusual amount of information on him related to his work with a satellite company.
Authorities are also going through hours of recordings between al-Hilli and his relatives and friends.
Police said the discussions shed light on the dispute between al-Hilli and his other brother, Zaid, over their father's will.
The victim's two daughters were the only survivors of the shootings. They are now in the care of a foster family, The Guardian reported.
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