First and foremost the expression of "native Algerians" is inaccurate as there were native Algerians of Arabic/Berber Muslim descent, native Algerians of Jewish descent, and native Algerians of European descent, which could all be born on French Algerian soil and were at some point in the history of French presence there treated differently.

From the earliest period of French presence in Algeria, there was recognition that the local population retained French nationality. As early as 1836, the Tribunal Supérieur d'Alger (the equivalent of a Cour d'Appel in the judicial system at the time) expressed that ^1 the population of Algiers could not be construed as retaining the status (qualité) of foreigners, as they obeyed the King of the French (Louis-Philippe was King of the French, not King of France) and recognized the same sovereignty as the French.

Later on, legal authorities had to establish a more detailed system to treat the varying situations. As early as 1865, the senatus-consulte of Jul. 14th 1865 established the civil status of Algerian muslims and the Algerian "indigenous israelite" population, indicating that, for Muslims, "while they are French, they should fall under islamic law for civil matters". This system mirrors the system still existing in the Indian constitution (as far as I understand it) where your religion defines the civil law applicable to your situation), inherited from the British colonial system. This senatus-consulte also allowed for Algerian muslims opting out of the Muslim civil law in favor of French civil law (coming from the "Code Napoléon"), but this was considered as akin to apostasy by some, and required administrative proceedings beyond the reach of the bulk of the native population, and as a consequence had very limited success. Unless they made such a demand (considered a form of naturalization) it was a constant jurisprudence of civil courts that while they retained the qualité de français (i.e. French nationality) they did not have citoyenneté française (i.e. French citizenship as that would have logically meant they fell under French civil law, and were granted full French citizen rights). This distinction will be maintained in the Statut Indigène law of 1881.

On oct. 24th, 1870, the Crémieux decree granted full French nationality and citizenship to the "indigenous israelite population"^2. They had been treated under French civil law (while not having full rights to vote and such) from the 1841 ordonnances^2b. This Crémieux decree faced antisemitic opposition from local europeans, and was repelled for a short period of time by the Pétain régime in 1940.

The distinction between French nationality and French citizenship will be maintained for Algerian muslims in the law of 1881, with a status gradually extended to most French colonies (statut indigène), with a dual system of French law for all matters not civil (in particular penal matters), and limited rights (and essentially exclusion from the national right to vote, and various civil liberties restrictions), and Muslim (or Berber tradition) law for civil matters. Muslims retained a limited right to vote, to elect representatives in the collèges musulmans of the municipal councils (which were a minority of the council, 20% until 1919 and 33% after, allowing for systematic French-citizenship of the mayor).

For penal matters, certain infractions were also treated differently for "indigènes" and citizens, with wide discretionary powers granted to local authorities for sanctions in a number of listed infractions (infractions spéciales à l'indigénat), without any guarantees regarding due process and the such, as detailed in the 1881 Code de l'indigénat^3.

Other colonies (in Africa in particular) retained a comparable system. This system was relatively costly regarding French administration authorities (it required a lot of manpower to run it) : in Indochina, the statut de l'indigénat was abolished after a short period in 1903^4 save for some regions. Do note that several parts of the French Empire were considered territories of French civil law, where the entire population retained full French citizenship : this is the case of all of current Départements d'Outre-mer and Tahiti, and the natives of the Etablissements Français de l'Inde that had renounced local civil law.

The code de l'indigénat penal system was abolished by the Lamine Guèye law of May 7th, 1946, and French citizenship was granted to local muslims by the ordonnance of March 7th 1944 (under the GPRF) and the law of September 20th 1947 (under the IVth Republic), while they retained local Muslim law (statut personnel coranique). This system (full French citizen rights, on a legal standpoint, and the option for traditional civil law) still exists in other French territories to this day (Wallis and Futuna, in the Pacific, and Mayotte, in the Indian Ocean, still have droit coutumier institutions). Finally, the principle of a collège électoral unique (i.e. participation in regular elections, on the local level) for Muslims, was put in place by de Gaulle by decree (Jul. 3rd 1958), with voting rights for Muslim women by the decrees of Jul. 3rd and Jul 12th 1958. They were able to vote in the referendum on the new constitution in September 1958 (with a turnout of 75%, and a wide majority in favor in Algeria, this was a major success for de Gaulle as the FLN had called for a boycott by Algerian Muslims).

The distinction between "French citizens with statut personnel coranique" and "French citizens under French law (de droit français)" was at the center of the Evian Accords in 1962, the first losing French citizenship and gaining Algerian citizenship, and the second retaining French citizenship.

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^1 : Tribunal supérieur d'Alger (aud. civ.) – 20 juin 1836, Dame Hamdan Bourkaïeb c. Moustapha ben Ahmed ben el Adgi Sehid, dans Robert Estoublon, Bulletin judiciaire de l'Algérie : jurisprudence algérienne de 1830 à 1876, t. 1 : 1830-1848, Alger, Adolphe Jourdan, 1890, 25 cm (notice BnF no FRBNF30408286), année 1836, p. 15-17.

^2 : Patrick Weil, Qu'est-ce qu'un Français : histoire de la nationalité française depuis la Révolution, Paris, Grasset, 2002

^2b : Valérie Assan, Les consistoires israélites d'Algérie au xixe siècle : l'alliance de la civilisation et de la religion (texte remanié de la thèse de doctorat en histoire préparée sous la direction de Catherine Nicault et soutenue en 2010 à l'université Paris-I / Panthéon-Sorbonne), Paris, Armand Colin, coll. « Recherches », juin 2012

^3 : https://fr.wikisource.org/wiki/Loi_du_28_juin_1881_qui_conf%C3%A8re_aux_administrateurs_des_communes_mixtes_en_territoire_civil_la_r%C3%A9pression,_par_voie_disciplinaire,des_infractions_sp%C3%A9ciales%C3%A0_l%27indig%C3%A9nat

^4 : Sylvie Thénault, Violence ordinaire dans l'Algérie coloniale, Odile Jacob, 2012, page 186