Military action, however, risks further inflaming relations with the U.S., which allied with the Kurdish-led Syrian Defence Force in its campaign against Islamic State.
Foreign minister Jean-Yves Le Drian said France was deeply anxious by the "brutal degradation of the situation" in flashpoints like Afrin - where Turkey has launched its operation - as well as Idlib and Ghouta.
Speaking to Asharq Al-Awsat, a Kurdish official linked Russia's approval that Ankara uses its warplanes with the withdrawal of Syrian opposition factions from the airport of Abu Duhur in Idlib.
The group controls Afrin, in Syria's northwestern corner, as well as a swath of territory along Turkey's border.
On Monday, Erdogan accused the United States of creating an "army of terror" in Syria along the border with Turkey, a reference to plans by the US -led coalition to transform some of the SDF forces into a 30,000-strong Kurdish-led border security force in Syria.
Among the targets hit was the YPG-held Minnigh military airport north of Aleppo, the army said.
Last month, the Turkish leader said he would not rule out the possibility of repairing ties with the Damascus regime, whose downfall he expected and supported since the onset of the Syrian civil war in 2011. The Russian military is believed to have a presence in Afrin.
In a stark warning to Turkey, Syria said on Thursday said its air defense would shoot down any Turkish jets that carry out attacks within Syria.
President Recep Tayyip Erdogan had repeatedly vowed that Turkey would root out the "nests of terror" in Syria of the People's Protection Units (YPG) militia which Turkey deems a terror organisation. The town has since emerged as a model for USA -backed Kurdish rule of largely Arab areas.
The operation opens a new front in Syria's war and sees Ankara confronting Kurds allied to the United States at a time when Turkey's relations with Washington are reaching breaking point.
"These internal forces are focused on preventing the flow of terrorists across borders, thus bringing more stability to the region".
Earlier on Saturday, the military said it hit shelters and hideouts used by the YPG and other Kurdish fighters, saying Kurdish militants had fired on Turkish positions inside Turkey. Turkish officials say rockets coming out of Syria killed one and injured 32 in the border town of Reyhanli.
It has also supported rival Syrian rebels and independently fought to drive IS from parts of Syria. Artillery shelling could be heard in the distance.
Turkey has prepared around 10,000 Syrian fighters to storm Afrin, according Rami Abdurrahman, director of the Syrian Observatory for Human Rights, a Britain-based monitoring group. Another commander said hundreds more were stationed in Atmeh, south of Afrin.
A United Nations official confirmed the release, explaining that they were mostly civilians who were kidnapped by rebels in the suburbs east of the capital.
Erdogan's comments followed the US-led coalition's announcement that it would train 30,000 fighters from the YPG-dominated SDF to act as a "border force" in northern Syria.
El Deeb reported from Beirut.