Arab refers to the people living in the Arabic world. If you were to bind it by an ethnicity, most of the people living in the Arab world "Today" would not be Arabs.
From Wikipedia: Arabs are a population inhabiting the Arab world.
namirez's point is that the historical people mentioned are Persians being called Arabs. And there are Persians that would take offense to this association.
Much of North Africa is considered part of the Arab world today, as it often refers to places where a dialect of Arabic is spoken and the culture has been affected in parallel. This is a key difference as Persian isn't even considered to be in the same language family as Arabic, unlike the dialects of Arabic that are predominant in the region approximately spanning Morocco to Egypt.
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.
From Wikipedia: Arabs are a population inhabiting the Arab world.