My head is hurting now
I've read the Wikipedia article about the Berber calendar. It looks like it's based on the Julian calendar. My guess is that the Algerians would have used the Berber calendar to calculate when to plant and harvest, and the calendar of their own religion to calculate when to celebrate feast days (the majority religion being Islam, but there were also Christians and Jews in the city).
Algiers at the time was a dependency of the Ottoman Empire and was very multicultural, including Turks, Arabs, Berbers, Jews, Europeans, Sub-saharan Africans, and probably some people I've forgotten.
My only consolation is that my MC will initially be as confused as I am. At one stage, he realizes that he's missed Lent (he's a Catholic) and that he's not sure exactly what age he is.
It's probably not necessary to know exact dates for every scene, but I at least need to know what season it is. So at least I know that this particular
Eid al-Adha doesn't occur in mid-summer (so I can ease up on descriptions of intense heat and sweaty hand grabbing the sheep's fleece) and I can have my MC think about Christmases past (how they involved more snow and significantly less mutton).