Or was Algeria so autonomous that the French conquest hadn't damaged relations with Constantinople at all?
That's a really unusual and interesting question. I have never seen it put quite like that! I think the short answer would be that the Ottomans saw the Russians as a greater threat than the French. Also, the Ottomans themselves had been occupiers of Algeria, and were not indigenous to the area.
You can read more about this in Andrew Hussey's excellent 'The French Intifada' that goes into some detail into the nature of Ottoman rule in Algeria and the French conquest.
Alternatively, feel free to follow my new blogs on Algerian history that are starting to appear at: