France has now raised its bird flu threat level
French officials raised the bird flu threat to high from moderate after the tests near the German border.
This is only the second outbreak of H5N1 in France. Early last year, 62 wild birds died of the virus in the centre of the country.
Nearly 200 people have died from the H5N1 strain worldwide.
Authorities in France had been carrying out tests on wild birds over the past week in several locations in the east.
The three swans that tested positive for H5N1 were found dead in a pond near the town of Assenoncourt.
With the elevation of the bird flu threat, domestic birds nationwide will be protected from contact with wild birds.
Last month the virus was found on two poultry farms in the Czech Republic.
Outbreaks were reported last year in 13 European Union countries, although none has yet resulted in human deaths.
The virus is highly contagious to birds.Although experts say the disease cannot easily jump the species barrier, there are fears it will mutate into a virus that can be transmitted from human to human.