This all started after the meeting between Macron and the SDF on 29th of March, when a Kurdish leader claimed the French President promised to send troops to Manbij, a Kurdish-Arab town that is under threat of a Turkish military operation.
France has denied the claims, saying there's no plan for unilateral operations in Syria outside the International coalition.
During the meeting on Thursday, Macron also renewed its political support for the SDF and offered to mediate a truce between the group and Turkey.
However, the offer was immediately rebuffed by President Tayyip Erdogan. In a speech, he said Macron had overstepped and that Turkey will never negotiate with terrorists. The People's Protection Units, or YPG, a group that makes up the bulk of the SDF, is considered a terrorist organisation by Ankara.
Diplomatic relations strained
According to Emre Demir, a Paris-based Turkish journalist, this episode will certainly sour relations between the two countries.
"Erdogan really believes Macron can change the military relationship between Turkey and the West," he explains. "Actually Ankara saw the Macron administration as an alternative to Merkel's Germany because relations between Germany and Turkey are not going well right now. This meeting sent shock waves to Ankara, they were expecting a different attitude from France," he says.
Demir also says this will impact Turkish aspirations in the region. "This is still a vague promise but it has certainly created a major obstacle for Ankara's political goals."
As for General Dominique Trinquand, former head of the French military mission to the UN, the move by Macron shows that France is willing to be more active in Syria.
"I think the aim is really to go back to the diplomatic scene and the politics in Syria. France has been absent from this strategic scene for the last seven or eight years. So it wants to go back inside, which is a very complex situation, but of major importance for the neighbors, mainly for Lebanon."
The controversy comes exactly as U.S. President Donald Trump claimed the U.S. could withdraw from Syria very soon. During a public address to industrial workers in Ohio, Trump said the IS was almost entirely defeated and claimed the U.S. should let other countries take care of the situation.
Analysts say the timing of both statements, from the French and the American presidents, is no coincidence, but they are not sure France could in fact fill the U.S. shoes. According to Trinquand, France does not have the resources to lead and so the coalition would have no future without Washington.
"I see what Macron did yesterday as rather an opportunistic signal by France that if the U.S. steps down France would be willing to be more prominent and present. But frankly, France doesn't have the ability and I don't think Europe has the stomach to do too much more," William Jordan, a Paris-based retired U.S. diplomat.
"I suspect despite whatever rhetorical flourishes that might be going on at the moment, the rest of the West will do what it has been needing to do for a long time, which is to remain focused on the refugees and the other security implications of continued unrest in Syria," he continues.
Jordan also says it is premature to be talking about the US leaving the coalition, but that pressure could mount in the future for such a move.
"That underscores how much of an improvisational aspect there is to much of what the Trump administration is trying to do in Syria. The reality, as I see it, is that the administration remains totally focused on countering the Islamic State, but beyond that it doesn't really have a vision to what it wants to happen in Syria in the next two years. The continued presence of the United States without a more clearly defined presence is untenable. So at some point the pressure will be on the U.S., even internally, to get out," concludes Jordan.