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The police made their arrest in Glasgow following a tip off in their search for Xavier Dupont de Ligonnes, the source said.
Officers had earlier picked out the suspect at Paris' Charles de Gaulle airport as he prepared to board a flight to the Scottish city.
After the plane landed he was fingerprinted, Scottish police said. French police said the fingerprints identified him as Dupont de Ligonnes, French sources close to the investigation told AFP.
Dupont de Ligonnes, who was the subject of an international arrest warrant, evaded a police dragnet in the Var region of southern France in January last year after witnesses reported seeing a man ressembling him near a monastery.
A businessman from an aristocratic family, he is suspected of murdering his wife and their children in the western city of Nantes before burying them under the terrace of their elegant townhouse.
French prosecutors said he killed his victims in a "methodical execution", firing two bullets from a silenced weapon at close range into their heads, before he rolled them in lime and buried them under cement.
Dupont de Ligonnes reportedly told his teenage children's private Catholic high school that he had been transferred to a job in Australia.
He allegedly told friends he was a US secret agent who was being taken into a witess protection programme.