Bianchi, who crashed during last month's Japanese Grand Prix, remains in a critical condition with severe head injuries, his parents said in a statement on Wednesday.
The 25-year-old Bianchi lost control of his Marussia car and hit a mobile crane that was inside the trackside barriers.
"Following a challenging period of neurological intensive care, we are able to announce that Jules has made an important step," the statement from Philippe and Christine Bianchi said.
A three-person team at Nice's neurosurgery service will now take care of him.
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"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," his parents said.
"We owe the medical staff (in Japan) 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."
At the Monaco GP in May, he secured the Marussia team's best ever result with a ninth-place finish.
In rainy, gloomy conditions in Suzuka on Oct 5, Bianchi's car slid off the track and ploughed into a crane picking up the Sauber of German driver Adrian Sutil, who had crashed out at the same spot one lap earlier.
Brazilian driver Felipe Massa, who survived a life-threatening accident in 2009, called it "the worst race of my life."
A 10-man working group was set up to review the accident and will present its findings on Dec 3.