Later addressing a joint press conference with his Saudi counterpart Adel Al-Jubeir, Le Drian commended Saudi Arabia's leadership in the fight against terrorism.
Tillerson concluded his mediation efforts Thursday, making no promise of an imminent breakthrough but voicing optimism that Qatar and its neighbors might soon be willing to talk face to face. The Qatari government has denied the accusations, blasting the blockade as "unjustified" and a violation of worldwide law.
On Saturday, Le Drian started his two-day visit to Qatar, Saudi Arabia, Kuwait, and the United Arab Emirates in order hear the positions of the states on the ongoing diplomatic row as well as to offer France's contribution to the mediation efforts led by Kuwait, according to the French Foreign Ministry.
After his visit to Qatar, Le Drian headed to Saudi Arabia where he met Crown Prince Mohammed bin Salman. Kuwait has been playing the role as a regional mediator since the rift erupted which marks the worst crisis in the GCC history since Iraq's invasion of Kuwait in 1990.
Qatar has rejected the demands, saying that the list in its entirety infringes on national sovereignty.
Qatar, a country with a negligible soccer background or infrastructure, was a controversial victor of the right to host the 2022 World Cup, which will be held in November and December to minimise the impact of the desert state's harsh climate.
Earlier in the week, U.S. Secretary of State Rex Tillerson was in the Gulf.
"We are heading toward a long estrangement", UAE Minister of State for Foreign Relations Anwar al-Gargash wrote on Twitter.
Qatar hosts some of the movement's prominent figures, including the spiritual leader and Egypt-born Yusuf al-Qaradawi.