When news of the arrest in Paris first broke, rights groups and Khashoggi's fiancée had expressed relief that such a high-profile suspect had been caught.
A 2019 UN investigation report said Al-Otaibi was a member of a 15-man Saudi team involved in killing Khashoggi after the journalist went to the Saudi Consulate in Istanbul to obtain a document to allow him to marry his fiancée.
The arrest had come at a sensitive time for the countries involved.
President Emmanuel Macron had days earlier become the first major Western leader to hold face-to-face talks with Prince Mohammed in the kingdom, a major buyer of French arms, since Khashoggi's murder.
Macron considers Saudi Arabia vital to help forge a region-wide peace deal with Iran, as well as an ally in the fight against Islamist militants from the Middle East to West Africa, and a rampart against the Muslim Brotherhood.
Turkey initially sought to pile international pressure on Prince Mohammed after Khashoggi's murder, saying the order had come from the highest level of the Saudi government, but Ankara has recently appeared to favour mending relations.