The Turkish offensive "endangers peace and stability in this region," the rebels' representative in France, Khaled Issa, said at a press conference in Paris on Monday. "France could take another step forward. It has already called for an exceptional [UN] Security Council meeting but it could do a lot more."
Turkey launched Operation Olive Branch on 20 January.
It is targeting areas held by the People's Protection Units (YPG), which the US-led coalition backed in its fight against the Islamic State (IS) armed group but Turkey regards as an extension of the Kurdistan Workers' Party (PKK), which has been fighting the Turkish state for three decades.
President Recep Tayyip Erdogan on Tuesday told the Turkish parliament that their forces, which have enlisted the help of the rebel Free Syrian Army, will lay siege to the town of Afrin in the next few days.
France called for restraint
France should call for international observers to be sent to the area and call for a "total halt to the aggression and the withdrawal of the Turks from the region", Issa said.
Paris and Washington have called on Turkey to exercise restraint and limit the operation to securing its borders.
Macron last week said it was "clear that the border is at risk" and that France "takes the security interests of Turkey, which is an ally, into consideration".
But, he added, "I don't consider that on the ground the international coalition's allies in the fight against Daesh [IS] have been abandoned."
An appeal by about 40 senators last week called on France to "break the deafening silence" of the international community "faced with this war of aggression" and called for the Turkish army' immediate retreat.
Kurds from across Europe demonstrated against the offensive and for the liberation of PKK leader Abdullah Ocalan in Strasbourg on Saturday.
French nationals to be judged
At the Paris press conference Issa insisted that French alleged IS members captured by the YPG will be judged by "competent authorities".
In January, lawyers representing five women being held by the Kurds made a legal complaint for "arbitrary detention", arguing that they were being held "without right or title" since Syrian Kurdistan has "no legal existence".
"Everybody should bear in mind that these alleged terrorists who came to our country did not come to bring us flowers, milk for our children or medicines," Issa said. "They gambled, they lost."
Macron has said that sentences passed on the French nationals could be adapted if they are not compatible with French law, although the authorities appear reluctant to have them returned to France.