Bianchi, who suffered the most serious F1 race injury since Ayrton Senna died in 1994 when he crashed into a recovery tractor in the wet at the Japanese Grand Prix on Oct. 5, has been transferred from Yokkaichi to a hospital in Nice.
"Almost seven weeks after Jules' accident at Suzuka Circuit, and following a challenging period of neurological intensive care, we are able to announce that Jules has made an important step," the statement read.
"Jules is no longer in the artificial coma in which he was placed shortly after the accident, however he is still unconscious. He is breathing unaided and his vital signs are stable, but his condition is still classified as 'critical'."
The family said the driver's recovery had entered a new phase concerned with "the improvement of his brain function" and his condition had improved sufficiently for him to be transferred back to France, where he arrived on Wednesday.
"We are thankful that the next phase of Jules' treatment can continue close to home, where he can be surrounded and supported by his wider family and friends," the statement added.
"We have nothing but praise for the outstanding care provided by the Mie Prefectural General Medical Center since the accident. We owe the medical staff there an enormous debt of gratitude for everything they have done for Jules, and also for our family, during what is a very difficult time for us."
Image: Jules Bianchi
Photograph: Mark Thompson/Getty Images
Davis Cup: Federer injury and spat hit Switzerland's chances
F1 Pitlane Tales: McLaren ready to debut new Honda engine
Drivers seek respite on track as Russia makes F1 debut
Marussia F1 team shuts shop while Caterham appeal to fans
Formula One: 'Bianchi crash was bad luck'