Gendarmerie sources in Brittany said the case was being treated as a "kidnapping" under French law.
The court at Guingamp in Brittany issued an arrest warrant for Ms Allen on Thursday night after she failed to obey a judicial order - upholding a decision by a British court - to return the boy to his father.
Gendarmes arrested Ms Allen's companion, Ismay Tremain, on Thursday afternoon and kept him in the station at Callac, near Guingamp, for questioning overnight. He was released yesterday.
Ms Allen appeared briefly at the Guingamp court on Thursday morning but left before the judgment that ordered her to return Gregory to Britain.
During the afternoon, gendarmes, accompanied by Mr McEwan, visited the house where Ms Allen and the boy have been staying, in the village of Bulat Pestivien, south of Guingamp. There was no sign of the mother or child but Mr Tremain was taken in for questioning.
The 13-year-old boy was supposed to have been returned to his father on 16 August after spending six weeks on holiday with his mother. A British court had earlier granted Mr Mc-Ewan sole and permanent custody of the child.
The Gungamp court confirmed this decision under French law, basing its judgment on article 12 of the Hague Convention, guaranteeing mutual respect of court decisions on family questions.
Mr McEwan is well known in France. His novel A Child in Time won the Prix Femina for the best foreign novel in 1993. The book, about a child whose custody is disputed by his parents, was translated into French under the title L'enfant vole (The Stolen Child).
Mr McEwan and Ms Allen used to live near Montpellier in the south of France but Ms Allen moved to a converted farmhouse in the centre of Brittany when the couple separated two years ago.
She said last week that she had registered Gregory to start school in Callac, six miles from her home, next Monday.Reuse content