The French Finance Committee said the government computers were expected to be back online Monday, Radio France Internationale reported.
Hackers using Chinese Internet addresses were apparently looking for documents relating to a G20 meeting held in Paris last month, although the attacks began in December.
French Budget Minister Francois Baron said investigators were following leads into the attacks. He said the "spectacular" attacks likely marked the first time the government's computer system had been breached on such a large scale, RFI said.
The attacks initially targeted about 150 computers but 10,000 were temporarily shut down as a precaution.
Dominique Lamiot, secretary-general of the finance and budget ministries, said the breach would cause France to improve its computer security.
Paris Match said the finance ministry has been under sustained cyberattacks since December.
The G20 is hosted on a rotating basis by several countries, most of them members of the European Union. France is the host nation for 2011.