He was arrested 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.
"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.
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.
- AFP