As of Tuesday morning, the petition had 9,331 signatures on change.org.
The petition attacked Turkish President Recep Tayyip Erdogan for strengthening ties with Islamic terrorist organizations, such as Hamas and Syrian militant groups.
In recent weeks, Erdogan has called for a boycott of French products and said that French President Emmanuel Macron "needs mental checks." France has recalled its ambassador from Ankara as part of the dispute between the two nations.
"Just like they say 'Don't buy goods with Turkish brands' in France, I am calling to all my citizens from here to never help French brands or buy them," Erdogan said.
France is the 10th biggest source of imports into Turkey and the seventh biggest market for Turkey's exports, according to Turkey's statistical institute. Among major French imports, French autos are among the highest selling cars in Turkey.
"French citizens defend the values, Liberty, Equality, Fraternity," read the petition. "This is something President Erdogan has made sure his people do not have."
"We will not fight hate with more hate. We will not create provocations," the petition continued. "Terrorists operate with funding from terrorist friendly states like Turkey. We will use our powerful and effective non-violent tools to cut Erdogan's funding, so that he can never cut our heads off again."
"By signing this petition, we will reaffirm that we are NOT supporting Erdogan's foreign policy," concluded the petition. "We pledge not to buy any products made in Turkey until it stops inciting hatred against Christians by Muslims."Armenia, Greece and Saudi Arabia have all limited or banned Turkish products.
Macron, who led a tribute to a history teacher beheaded last month by a Chechen teenager for showing caricatures of the Prophet Mohammad in class, declared war on "Islamist separatism," which he believes is taking over some Muslim communities in France. The French president refused to denounce caricatures of the Prophet Mohammad during the tribute.
The comments sparked protests around the world. France has been hit by a series of terrorist attacks targeting civilians and religious sites since.
Reuters contributed to this report.