"It would be preferable if the parties could engage in a process of de-escalation, one that is indispensable so that negotiations can take place in a constructive atmosphere," Le Drian said in Abu Dhabi.
He held talks with Abu Dhabi Crown Prince Sheikh Mohammed bin Zayed al-Nahayan, who is also deputy commander in chief of the UAE's armed forces.
Abu Dhabi was the last step in a tour of four Gulf nations that began Saturday and also took Le Drian to Qatar, Saudi Arabia and Kuwait.
Earlier Sunday, the French foreign minister held talks in Kuwait City with senior officials in a bid to bolster the emirate's attempts to mediate in the Gulf crisis.
Le Drian met with the emir, Sheikh Sabah al-Ahmad Al-Sabah, and Kuwait's foreign minister, state news agency KUNA said, for talks on a regional rift which has seen Saudi Arabia, the United Arab Emirates, Egypt and Bahrain sever all ties with Qatar.
The French foreign minister has supported Kuwait as a mediator in the crisis, which he said should be resolved "by the Gulf countries themselves".
"France does not want to substitute the mediator," Le Drian said in Saudi Arabia on Saturday. "It wants to be a facilitator by joining efforts of other countries."
Le Drian's visit comes after a four-day mediation mission by US Secretary of State Rex Tillerson ended on Thursday with no announcement of progress towards defusing mounting tensions in the Gulf.
Saudi Arabia and its allies imposed sanctions on Doha on June 5, including closing its only land border, denying Qatar access to their airspace and ordering their citizens back from the emirate.
The four Arab states accuse Qatar of ties to Iran and of funding Islamist extremist groups. Qatar has denied the accusations.
The Gulf crisis is the worst to hit the region since the establishment of the Gulf Cooperation Council in 1981.