It's very hard for me to find the borders for French Egypt during the time of Napoleon 1798-1803.
Specially the southern borders of Egypt where did they go?
History Stack Exchange is a question and answer site for historians and history buffs. It only takes a minute to sign up.Sign up to join this community
Immediately prior to the French Invasion, Egypt was part of the Ottoman Empire, which stretched roughly to the modern boundary of Libya in the west, the first cataract of the Nile, and down the Red Sea coast to roughly the boundary of modern Somalia.
However, the African boundaries of the Ottoman Empire at this time were mostly a polite fiction, and Egypt proper (from the mouth of the Nile down to the first cataract) was effectively ruled during this period by either Mamluk descendants, or whatever strongman or adventurer managed to scrape up enough forces to push the former out, for the honor of paying nominal tribute to Istanbul.
When the French took over, we know their control didn't even fully extend to the first cataract for the following reason: When the French won the Battle of the Pyramids, the opposing survivors retreated upriver and fought a guerrilla campaign from there.
Colin McEvedy's Penguin Atlas of African History has a map of 1800 (which I sadly couldn't find online) showing the result. Basically the controlled portion of Egypt was just Alexandria and the Nile below the 1st cataract. The area between that and Libya was effectively uncontrolled, as was the Nile between the 1st cataract and the Funj territory up above the 6th cataract. The Red Sea coast remained as much Ottoman territory as it was before Napoleon's little adventure.