Bloodstains found in the family's house near the city of Nantes match the DNA of three of them, officials say.
There has been no activity in any of their bank accounts or mobile phones since they disappeared, they add.
A document and a pair of trousers of one of the missing have now been found some 300km (186 miles) from Nantes.
The Troadec family - Pascal and Brigitte, both aged around 50, their son Sebastien, 21, and daughter Charlotte, 18 - were last seen on 16 February. Authorities were informed of the family's disappearance by Brigitte's sister.
Investigators searched their two-storey house and found bloodstains matching DNA of the parents and Sebastian, but not of the daughter.
Traces of blood were found on Sebastien's phone, on Brigitte's watch and under the stairs, and it appeared that someone had tried to wipe them away, prosecutor Pierre Sennes said.
The beds had been stripped, with some sheets drying on an indoor rack. Wet clothes were still in the washing machine and food was going off in the refrigerator.
"It's as if the life of the house was frozen in time," Mr Sennes said.
The family's two cars were still parked in front of the house but investigators have not yet found Sebastien's car.
On Wednesday, a social security card and a pair of trousers belonging to Charlotte were found near the city of Brest. But authorities have not released more details.
Reports suggested the father once suffered from depression while his son had psychological problems.
Sebastien had been sentenced to carry out community service after being convicted in 2013, when he was a minor, of making death threats on his blog, Mr Sennes added.
French newspaper Le Monde reported that Sebastien had posted on a video game online forum: "What do I hate the most? My reflection." And: "What makes me sad? My life."
And on Twitter, he had written: "If you really knew what was going on in my head, you would think I was a crazy person with no morals."
An investigation into murder, abduction and illegal confinement has been opened, the prosecutor says.
Local media have compared the case with a murder of five members of the same family also in the region of Nantes, in 2011. The father, Xavier Dupont de Ligonnes, is a suspect and is still at large.
French police have opened a murder investigation into the mysterious disappearance of a family of four in western France two weeks ago.