Hundreds of hens were killed after the virus was detected in a garden centre on the French island of Corsica, and the Danes said more than 25,000 birds would be slaughtered after the virus emerged in the west of the country.
France has ordered national protection measures including obligatory confinement of poultry to isolate them from wild birds, while Denmark has suspended exports of eggs to chickens outside the EU.
The virus, which is not harmful to humans but is potentially devastating to the farming sector, has so far appeared in Belgium, the Netherlands, Russia, Ireland and Britain among other countries.
Dutch officials said earlier this month they had culled more than 200,000 birds.
Duck breeders in southwestern France have been hit twice in recent years, sparking mass culls that cost producers hundreds of millions of euros.
French officials insisted there was no need for people to change their habits.
“The consumption of meat, foie gras and eggs – and more generally of any food product – does not present any risk to humans,” the ministry said.
Denmark urged farmers to ensure the birds were protected from possible infection.
The Danes are culling the country's entire population of fur farm mink after some were found to be infected with the novel coronavirus.