It began with centuries of piracy and enslavement in the Mediterranean sea, leading to the https://en.wikipedia.org/wiki/Barbary_Wars , which in turn led to the https://en.wikipedia.org/wiki/Bombardment_of_Algiers_(1816) . All this doesn't set a path for the invader to offer equal rights to the "indigenous" population.
A military action, even a colonial invasion, to "pacify" a place and to take control of it has little to do with a full annexation. The US did not make Afghanistan a State... And even among European colonial empires Algeria is quite unique.
France had lost most of its Empire during the Revolution and Napoleonic period so was keen to rebuild one. France did not have a settled Canada or Australia, either, so perhaps this also played a role but it seems unrealistic to believe that trying that with an Arabic Muslim country could have ever worked.
Indeed. No objective is intangible. Actions taken to reduce an aggressive enemy to inaction can lead to a promising discovery (in this case, that of what would become Algeria, which was then a rich agricultural and pleasant territory occupied by non-unified tribes) leading to a desire to seize it.