Turkey and Armenia are at odds over how to describe treatment of Armenians during the Ottoman era in WWI, with Turkey denying massacres and forced deportations amounted to a genocide.
French President Emmanuel Macron in February announced France would hold a national day on April 24 to commemorate the "Armenian genocide", drawing criticism from Ankara.
During a meeting of the NATO parliamentary assembly in Antalya in southern Turkey on Friday, Turkish parliament chief Mustafa Sentop lashed out at France's decree to establish the commemorative day, accusing Paris of "manipulating history."
He also referenced massacres committed in Algeria when it was still a French colony and in Rwanda whose government accuses Paris of being complicit in the 1994 slaughter there.
Attending the meeting, French lawmaker Sonia Krimi, from Macron's LREM party, criticised Turkish comments saying she was shocked. But that provoked a sharp response from Cavusoglu.
"In terms of genocide and history, France is the last country to be giving lectures to Turkey, and we have not forgotten what happened in Rwanda and Algeria," the minister said.
"You can keep trying to look down on us, but we will keep putting you in your place."
Krimi and the French delegation left the room in protest over Cavusoglu's remarks.
"When the arrogant @MevlutCavusolgu gives you lessons on arrogance and politeness, arrogantly and without any respect," she wrote on Twitter referring to the incident.
Turkey's presidential spokesman Ibrahim Kalin hit back posting on Twitter a story from state news agency Anadolu about "dark stains in French history."
"Neither their colonial past nor their self-centred present guarantees their moral superiority," he wrote.
Armenians commemorate the massacres on April 24 -- the day in 1915 when thousands of Armenian intellectuals suspected of harbouring nationalist sentiment and being hostile to Ottoman rule were rounded up.