CLICHY-SOUS-BOIS, France — In the aftermath of the Charlie Hebdo attacks, France has begun a defensive but potentially decisive debate over what it means to be French — and whether that definition can make room for its vibrant, growing Muslim population.

At its core, the debate is about whether the French sense of identity has become so intertwined with secularism that the country is failing to honor its ideals as it becomes a multicultural society in which Islam is taking a more prominent place.

By law and tradition, citizens are meant to be judged as individuals without reference to race, religion or gender in the service of the republic’s ideals and its motto: Liberty, Equality, Fraternity. That aspiration, dating to the French Revolution and deeply embedded in French life, was given a powerful voice in the large demonstrations of national unity following the January killings of cartoonists, police officers and Jews by homegrown Islamist radicals.

But these ideals, and the French Republic itself, can feel distant and empty to disaffected Muslims, who traditionally see little distinction between religion and public life. They often view the state’s values as foreign, even blasphemous, imposed on them like a form of cultural colonialism, and sometimes used as a pretext for racial and religious discrimination.