About the Muslim population, OTL Napoleon did try to launch himself as some sort of "protector of Islam". If he should recruit among the Copts, there is of course the danger that this might be seen by the Muslim population as a potentially dangerous development and it could be used by the Ottomans to launch a "holy war against the crusaders". Copts might be among the soldiers, but I doubt that tehy would be a dominant group.
Indeed. The Copts would also be suspicious of a foreigner. Italian, French, Catholic, aethist, revolutionary, crusader, conquerer, one of the main issues is that he is foreign and they have no idea if he would stay around or not. Besides, the Copts had a strong interest in staying alive and in Egypt. Yes, Napoleon might miraculously get the urban Coptic men to take up arms (if they had any) and somehow get some training. I doubt they would very much desire to leave Egypt, though. It would mean leaving their women, children, elders, and property behind while (depending on the political route Napoleon takes) would make them all look like traitors. Better to keep their heads low. The Shias and Sunni of various sorts historically went back and forth in owning Egypt and it was a rather wealthy area. I think their best hopes is to be productive tax payers. Having the Copts join their neighbors to fight back against the Mamluks in alliance with the French might not be out of the question, as the Mamluks were fairly rotted (apparently after they felt Cairo they attacked a caravan on the Haiji to replenish their supplies) but what good they would do is still a question.
I actually wonder if someone could get something similar to an Islamic Republic set up. Lots of imams acting as judges for rural affairs, civil administrators continuing their work (the Ottomans had local people do a lot of administration, part of why the Syrians were angry when the French said they were not ready for self-rule, despite having centuries of experience), and maybe a Khedive staying on top and focusing on expanding around the Red Sea. Though it probably would last about as long as most of the French backed Republics. Just until Nappy decides he wants a heavy golden hat and tries hollowing out the capstone of a pyramid and gilding it. I do wonder what he would loot artistically in Egypt. Lotta artistically valuable stuff around, but nothing exceedingly famous that wasn't under the Valley of the Kings.
And do you guys think he would go the route of trying to be a Roman Emporer of some sort there? Maybe Greeks? In real life when he became Emperor of the French he tried to be the successor of Caesar (one or another) instead of Charlamagne. Perhaps he tries being the heir of Alexander here? Then future generations can have him move into Greece and Syria like the Egyptians did. Plus Alexander was respected in Islam, so he might get kudos there if he made it stick.