PARIS—Diplomatic tension between France and Turkey rose Wednesday, after the French government said it backed a draft bill that would make it a crime to deny Armenians suffered genocide at the hands of the Ottoman Empire in 1915.

"The government backs the idea that genocides can't be denied," Budget Minister and government spokeswoman Valérie Pecresse said after the weekly cabinet meeting. "Each and every country must have the courage to... assess its history with lucidity."

The...