POD: Sometime in the 1860s, Napoleon III manages to establish a few 'native states' where the Colons do not hold sway (the catholic settlers annoy him, he was impressed by the Arab leaders, and in TTL he manages to get more support in the metropole). The Franco-Prussian war goes more or less as OTL, but the Arabs of Algeria invite him in rather tahn accept the domiance of the 'athiest' French Republic... while both the colons and a fair number of Royalists in the Metropole hold similar opinions.
There is a degree of population exchange, but the new government in Paris is happy to be rid of the royalist/colonialist embarassment in North Africa... and they throw in St. Louis and the other African ports in the bargain as the Imperial Court moves to Algiers.
The new 'Empire' is more-or-less a Dual Monarchy, but Imperial patronage and sheer numbers results in increasing Arab influence. All civil service is open to Muslims by 1880, and the right to have court cases heard in Arabic or French throughout 'l'Empire Outre-Mer' is established shortly afterwards.
The Bey of Tunis signs a treaty of vassalage of Sultan Nabuliun IV in 1885.
Now what?
HTG