Khaled Aedh Alotaibi was arrested at Charles de Gaulle airport in Paris on Tuesday, a police source told the BBC.
He is believed to be one of 26 Saudis wanted by Turkey over the killing.
A Saudi official later said the arrest was a case of mistaken identity, and that those involved in the murder had been convicted in Saudi Arabia.
Mr Alotaibi, a 33-year-old former Saudi royal guard, was travelling under his own name and was placed in judicial detention, RTL radio said.
Khashoggi, a prominent critic of the government in Riyadh, was murdered at the Saudi consulate in Istanbul in October 2018.
Saudi Arabia said the former Washington Post journalist had been killed in a "rogue operation" by a team of agents sent to persuade him to return to the kingdom.
But Turkish officials said the agents acted on orders from the highest levels of the Saudi government.
The murder caused a global uproar and damaged the image of Saudi Arabia's de facto ruler, Crown Prince Mohammed bin Salman. He has denied any role.