The court heard that the two primary school children were born in France, where they normally reside, to an Irish father and a French mother.
The two boys and their parents cannot be named for legal reasons.
The father returned to Ireland after the couple separated.
During a visit to Ireland last year, he decided not to return the children to their mothers due to rules in France requiring children over six to wear face masks at school.
While he did not want them to stay in Ireland permanently, the man argued that requiring them to wear masks would adversely affect one of his sons and cause him anxiety and distress.
Their mother, through French courts, filed a petition under the International Convention on the Civil Aspects of International Kidnapping, commonly known as The Hague Convention.
In a judgment delivered earlier this year, High Court Judge Mary Rose Gearty dismissed the father’s claims and ruled that the children had been wrongly detained and should be returned to France.
That decision was appealed by the father, who said he was seeking a stay until the face mask order in France was lifted.
In today’s judgment, the three judges of the Court of Appeal, consisting of Judge Mary Faherty, Judge Maurice Collins and Judge Teresa Pilkington, dismissed all of the reasons for the father’s appeal. .
Giving the court decision, Justice Collins said the evidence presented to the court was grossly insufficient to establish serious risk or harm to any of the children.
There was no plausible or significant evidence that the requirement to wear a face mask in school will have a negative impact on the child, the judge said.
He added that it was not disputed that the evidence required to order the return of the children under Article 12 of the Hague Convention had been satisfied.