Secretary of State Rex Tillerson just spent a week in the region trying to find a solution to the Gulf that began last month when Saudi Arabia, the United Arab Emirates and other Arab countries moved to isolate Qatar.
The bloc also issued a land, sea and air embargo on Qatari planes and ships. Prior to the dispute, Qataris could travel visa-free between the Gulf countries.
Le Drian was speaking alongside al-Thani, a few hours after his arrival in Doha.
The Qatari top diplomat, who will meet Erdogan later, said Doha was being subjected to an "unjust siege" imposed "without any reason".
French Foreign Minister Jean-Yves Le Drian called Sunday for de-escalation in the row between Qatar and four Arab countries, as he held talks in the United Arab Emirates and Kuwait, a mediator in the crisis.
On his previous visit on Tuesday, the USA and Qatar signed an agreement to combat terror funding, subsequently dismissed as "insufficient" by the Saudi-led states.
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Le Drian stressed that France wants a quick end to the tension and the blockade enforced. He is scheduled to visit the UAE and Kuwait next. The demands included shutting down the Doha-based Al Jazeera broadcaster, scaling back cooperation with Iran, closing the Turkish military base in Qatar, and paying an unspecified sum in reparations.
Its energy riches have transformed Qatar into one of the world's wealthiest countries, a major global investor and a regional player that will host the 2022 football World Cup.
"No country has the right to raise the issue of the Turkish base or the military cooperation between Qatar and Turkey as long as this cooperation respects worldwide law", Qatar Foreign Minister Sheikh Mohammed bin Abdulrahman Al Thani told reporters in Ankara.
The Saudi Arabia Minister for Foreign Affairs, Adel Bin Ahmed Al Jubeir, said that the foreign ministry will provide the French Ministry for Europe and Foreign Affairs with a complete file of negative actions carried out by Qatar over the years, referring to also providing the American side and other countries with the same file.
But after the top US diplomat left the region, the UAE state minister for foreign affairs went on a tweetstorm in Arabic, saying the rift is "far from a political solution" and that the countries face a "long estrangement".
Gargash also stated that the Arab states need to be convinced that Qatar is no longer a sponsor of terrorism.
Saudi commentators criticized the result of Tillerson's visit to Qatar, saying the signed agreement fell far short of the demands made for Qatar to change its policy of supporting Islamists.