The French prosecutor leading the investigation into a mysterious shooting, which killed three members of a British family in the Alps, says police are still puzzled about the deaths two months after the bodies were discovered.

"We are no further than day one," Eric Maillaud told BBC News. "For now, all lines of inquiry remain open."

Saad al-Hilli, 50, his wife Ikbal and her mother Suhaila al-Allaf, were shot twice through the head in their car. The daughters Zeinab, seven, was treated for bullet injuries while four-year-old sister, Zeena, survived after hiding beneath her mother’s body.

The family, who live in Claygate in Surrey, were on vacation when they were gunned down on Sept. 5.

French cyclist Sylvain Mollier was also shot dead nearby.

Maillaud told BBC News that after interviewing 800 people and following lines of inquiry in seven countries – France, Italy, Switzerland, the U.K., Sweden and Spain – there is still "no motive" for the killings.

Maillaud said police are looking for "someone who has killed before" and has no value for human life. Specifically, someone who could have psychiatric problems and has access to weapons – a hunter or a shooting club member.

He added that they are very sure that Mollier was not the target.

Maillaud also insists that it doesn’t look like the killings were done by a professional assassin since it seemed too messy, done with an old gun. A forensics team examined the shell casings, which suggest the gun was an antique, likely dating back to the 1930s.

No DNA was found at the scene —  which was in a remote area near Lake Annency, not far from the Swiss and Italian borders.

Police are still digging into al-Hilli’s background – first looking into a purported dispute with his brother over their father’s inheritance and the family’s Iraqi background.

Maillaud has said the investigation will be very long and he feels pressure, not from the public, but from a professional responsibility to the two girls.

"I don’t want to tell [them]… that we failed."