Would it have been plausible for France to beat Britain to Fashoda and thus conquer South Sudan and then, after its logistical situation in the area improves and Italy gets its butt kicked by Ethiopia, invade Ethiopia itself in order to create a land connection between its West African colonies and Djibouti?
If so, how would a Franco-Ethiopian War in the late 1890s have turned out? Also, please keep in mind that Ethiopia has just fought a successful war against Italy in this TL (in 1896, to be specific).
Any thoughts on all of this?