Doctors placed seven-year-old Zainab al-Hilli in an artificial coma following the murders last Wednesday to help her recover from a fractured skull.
Officials yesterday said she had regained consciousness but warned that she was still under sedation and her speech was not yet audible.
Her four-year-old sister Zeena, who survived unhurt for eight hours after the attack hidden beneath her mother’s body, has already been seen by police but was unable to provide any information.
It was not clear how long investigators specialising in dealing with child witnesses would have to wait before speaking to Zainab.
Annecy prosecutor Eric Maillaud, however, has said she was “extremely traumatised” and stressed that there was no question of rushing the process.
Zeena yesterday returned to Britain with relatives who had flown out to Annecy in southeastern France to collect her.
Saad al-Hilli, his wife Ikbal, an elderly relative and the two girls had been on a camping holiday on the shores of Lake Annecy when the tragedy happened.
Local cyclist Sylvain Mollier was also killed after apparently stumbling on the scene.
Police yesterday carried out a second day of searches at the family home at Claygate in southern England.
Hilli, a naturalised Briton of Iraqi origin, worked as a mechanical design engineer with the Surrey Satellite Technology firm.
His brother Said was also interviewed by police in Britain at the weekend after he came foward to deny reports of a financial dispute between the brothers.
The fact that each of the four victims was shot twice in the head has fuelled speculation that the killings were a professional hit.
But police in France say they are considering a range of possibilities.