Kuwait is trying to mediate the dispute.
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.
"France is calling for these measures to be lifted, especially the ones that affect the population (the Qatari population), specifically the measures that affect bi-national families". They are convinced that the terrorism they suffer from is due to Doha's support for it. "The second is to refrain from supporting extremism and from inciting and spreading hatred".
"Running local hospitals or schools, typical Brotherhood activities elsewhere in the region, is popular but inevitably undercuts the state's legitimacy".
While the six countries are unlikely to be under the illusion that Federation Internationale de Football Association will simply accept their demand, tabling it allows the Saudi-UAE-led alliance to assert that it is not backing down in the Gulf crisis and is increasing pressure on Qatar.
Tillerson met Qatar's Emir Sheikh Tamim bin Hamad Al-Thani for the second time in 48 hours, together with a Kuwaiti mediator, on the final leg of his trip.
"France is talking to all these countries to help in the search for a solution".
"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.More news: Iraqi intelligence refutes reports on IS leader al-Baghdadi's death
In his phone call with Sisi, Trump "reiterated the need for all countries to follow through on their commitments at the Riyadh summit (in May) to stop terrorist financing and discredit extremist ideology", the White House said.
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.
But after the top USA 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". Qatar says the allegations are based on lies.
The GCC members Kuwait and Oman have not cut ties with Qatar.
The Kuwaiti emir Sheikh Sabah said that despite the bitter feelings on both sides, he remained hopeful they could be made to fix "our Gulf home".
At the heart of the Gulf crisis, lies a fundamental divide in how Qatar and its main detractors, Saudi Arabia and the UAE, envision the future of the Middle East and North Africa.
Qatar said in late May that hackers had posted fake remarks by the emir, an explanation rejected by Gulf states.
The foreign ministers of the boycotting countries plan to meet in Manama to decide on their next steps.