French Prime Minister Francois Fillon has authorised the extradition to Italy of a former member of the far-left Red Brigades movement, the justice ministry said.
Marina Petrella was convicted by an Italian court in 1992 of offences including murder, kidnapping, attempted kidnapping and armed robbery.
She has a month to appeal to the State Council, France's top administrative law body.
The Red Brigades carried out a campaign of violence in the 1970s that culminated in the kidnapping and murder of former Prime Minister Aldo Moro in 1978.
Many former members took refuge in France where former Socialist president Francois Mitterrand refused to extradite left-wing radicals who renounced violence.
Petrella had started a new life in France with her partner, with whom she had a child.