PARIS — What propels Islamist terrorism and attacks against France is more than an academic debate: The answer shapes policy toward blunting the threat.

So it is no inconsequential matter in a culture under attack, and one that so cherishes its intellectual debates, that France’s two leading scholars of radical Islam — former friends — have turned bitter rivals over their differing views.

“Madman,” “thug,” “illiterate,” “paranoid,” “ass,” “not a thinker” — these are just some of the choicer insults the two men have hurled at each other in a peculiarly personal quarrel with far larger stakes that has reverberated through the French news media and society for months.

The two distinguished academics, Olivier Roy and Gilles Kepel, have long lists of books to their name, and years of field work in the Middle East, Central Asia and the troubled French suburbs. They are both eagerly consulted by the French news media and government officials.