The bodies of a five-year-old girl and a ten-year-old boy were discovered on Saturday afternoon in the man's apartment in Saint-Priest, a south-eastern suburb of Lyon.
The unemployed father confessed to the gruesome crime "but did not go into details of the motive", prosecutors said.
The tragedy was "linked to a bitter separation" and "the state of his visitation rights which he considered insufficient", another judicial source told AFP.
"In 2010, there was an incident of violence with his spouse which led to restrictions on his visitation rights," the source said.
He was arrested on Saturday evening in Lyon and placed in custody. A judicial official said a knife which is thought to have been the murder weapon had been found.
The man had visitation rights but only in the presence of another person, the official said, adding that this was the first time he had brought the children home to his apartment on the second floor of a four-storey building without a third party being present.
He remained in custody late on Sunday and was to be presented to a prosecutor on Monday when he was expected to be charged.
Police were also questioning his ex-wife, notably to learn more about "the legal framework of the children's visits to their father".
"We understand that a British national has been arrested in France," a Foreign Office spokesman told AFP. "We are in contact with the French authorities and we await the outcome of their investigation."
Several witnesses said the man fled on roller skates after his former wife encountered him on the stairwell of the building and saw him with bloodstained clothes. She immediately alerted the police.
A neighbour said the mother was soon joined by relatives, including her brother-in-law and the children's grandparents, and was lucid although in shock.
A psychiatrist from the emergency services was immediately dispatched to give her counselling.
"They were devastated but relatively composed," the neighbour said, speaking on condition of anonymity.
"She said: 'He has killed them'. I tried to comfort her saying we didn't know as yet although I knew at the bottom of my heart that they were dead."
Ahmed Benguedda, another neighbour, told AFP the couple had divorced "two or three years ago" and that the man had drinking problems and was a wife beater.
After the divorce the wife, who worked as an assistant accountant, moved out of the apartment they had jointly bought and was living in the Isere region of eastern France.
But the children were "well-balanced", said Benguedda, whose seven-year-old daughter often played with them.
"All the people in this building are in a state of shock," Benguedda said.
More neighbours were being questioned by the police on Sunday.