The 30-year-old victim lost both arms above the elbow after falling between a train and the platform at the Chambery station in the foothills of the French Alps in mid-August.
Quick-thinking medics who arrived on the scene shortly afterwards were praised for helping preserve her arms by wrapping them in sterilised material and ice before transferring them quickly to hospital.
Two hours after the accident, a medical team of 10 at a hospital in the nearby city of Grenoble began the operation to reattach the limbs.
"The muscles can't be reactivated completely so some movements will be problematic for the patient, particularly with her hands," surgeon Michael Bouyer from the CHU Grenoble Alpes hospital told reporters on Friday.
"But it will be much better than having a prosthesis".
The first operation to reattach two arms was carried out in Germany in 2008 and similar operations have been performed in China and India since.
Bouyer said the patient was "doing well" and, once recovered, would need between 18 months and two years of physiotherapy to regain movement in the damaged limbs.
By Benoit Pavan and Julia Pavesi