No, not like French. Around 85% of Moroccans are fluent in Moroccan Arabic and about 72% of Algerians speak Algerian Arabic, more than any other language (particularly Berber and French) in their respective countries as far as I can tell. A similar story exists in Tunisia, despite a majority of the country also apparently speaking French.

I think it's pretty fair to call these dialects of Arabic the predominant languages.