Let's just approach this as an ASB. Let's also assume North Africa is depopulated.
North Africa would become the first logical step. Presumably everything east of Libya will be settled from the Mediterranean. So you'd see an influx of people from Iberia, Italy, and the south of France into the area. I'd bet on most of the settlers coming from Castile, Naples, and Sicily. Venice and Genoa (and for that matter, Portugal) were looking for trade routes at this point, not new lands.
An interesting question is, whenever Granada gets fully conquered, what will happen to the Moors (and eventually the Jews) of Iberia?) I could see the different Spanish kingdoms expelling them to a "pale of settlement" in North Africa, as they would make useful frontiersmen. So you may still have some Muslims in North Africa after all. Perhaps even a Jewish kingdom, if you play your cards right.
The Ottomans are in the catbird's seat if they play their cards right as well. IIRC, there were still some Ghazi states in Asia minor in the way, but without Egypt the Syrian possessions of the Mamalukes should fall like a deck of cards. At which point, the Ottomans would be pretty well positioned to resettle the Nile with whichever ethnic group they wished. An interesting question will be if they'll consider Egypt part of "Europe" for tax purposes - which would allow Christians from the Balkans to settle the lands without fear of conversion, and also allow the Ottomans a hefty new tax base.
East Africa will probably be quickly resettled by Arabs of all stripes. If history unfolds anything like HE, Oman will be best positioned here. Unfortunately, I can't see China or any Indian state getting in the mix.
I don't expect South Africa to be too different from HE initially - the indigenous population was already sparse after all. Of course, there will be less resistance to pushing inwards once whoever establishes the cape consolidates there.
Going beyond this, it gets more difficult. Some predictions.
1. Ethiopia and the Sahel get settled, but beyond that there is minimal settlement in Africa until at least the 1800s - the New World is still far better after all.
2. Probably no coffee, as it was barely known of outside of Ethiopia at this point, if at all.
3. Obviously nothing resembling the HE slave trade. The cash crop economy in general is pretty screwed, and certainly delayed. With Africans gone, Native Americans rare, and Europeans not doing well in tropical climates, the whole area - but particularly the Caribbean islands, will be retarded in growth.
4. That is until someone gets the idea to import large numbers of plantation workers from India. This would still probably not be done until the 1800s, but even with that, they'd probably end up the predominant ethnic group through a wide band reaching from the Caribbean to West Africa. Would make for some interesting color lines.