The attack hit the post office earlier this week, affecting parcel deliveries during the busy Christmas period. The post office's mobile and banking services were also down for two days.
According to the Public Prosecutor's Office, the French intelligence service (DGSI) has taken over the investigation after the pro-Russian group Noname057 claimed responsibility for the attack.
The group has been accused of other cyber attacks in Europe, including in connection with a NATO summit in the Netherlands and against French authorities earlier this year.
France and other European countries that support Ukraine claim that Russia is conducting a campaign of "hybrid warfare" through, among other things, denial-of-service attacks to sabotage the countries.
