There is no indication that colonial authorities were concerned with the way Muslim Algerians named their children. In 1882, they had forced French-style name patterns (First name - Last name) on the local populations, which had been met with resistance and caused many problems, as the traditional naming pattern was quite different.

Decades later, part of the births and marriages of Algerian Muslims were still not registered properly, even in European population centres. Outside those centres, registers were held by Muslim officials. As a result, Algeria muslims could name their children with little or no oversight from the authorities, the only constraint being that the name follow the French pattern.

At least that was the case in Algeria. Algerian muslims who had immigrated in France seem to have been forbidden from giving Muslim names to their children by French authorities (given names were tightly regulated in France until 1993): this may have been a problem frequent enough that the Vichy governement in 1943 published a circular that specifically allowed the use of Muslim names for Algerian children born in France.

So, unless your grandmother was born in France (in which case having a French name would have been mandatory if the registrar had said so), your great-grandfather may have had personal reasons to give a French name to his daughter, and he would have been allowed to do it. Perhaps the name itself could shed some light: it could have been the name of someone famous, or someone he admired etc.

Sources

• Kateb, Kamel. Européens, “indigènes” et juifs en Algérie (1830-1962): représentations et réalités des populations. INED, 2001.
• “Quand une circulaire de 1943 donnait tort à la croisade de Zemmour contre les prénoms arabo-musulmans,” Oumma (blog), January 30, 2019, https://oumma.com/quand-une-circulaire-de-1943-donnait-tort-a-la-croisade-de-zemmour-contre-les-prenoms-arabo-musulmans/.