Africa is huge, but the following is for all of Africa – including the very popular Morocco-Algeria-Tunisia top.
There are many ways of looking at ‘biggest’: weekly frequencies; destinations served; ASK/ASM; FTK/M; number of seats each week.
In terms of European airlines to Africa by number of weekly seats (one way w/c 14th September 2016) and share of the market by seats available, the top-10 are:
Air France: 48,568 (8.59%)
Turkish: 40,044 (7.08%)
Ryanair: 29,673 (5.25%) – all the flights to/from Morocco
Aigle Azur: 22,146 (3.92%) – North Africa
British Airways: 19,940 (3.53%)
Jetairfly: 18,040 (3.19%)
KLM: 17,698 (3.13%)
Lufthansa: 14,604 (2.58%)
Transavia France: 14,553 (2.57%) – North Africa
If it’s widened to include all airlines between Europe and Africa by weekly one-way seats, the top-10 is somewhat different:
RAM: 52,477 (9.28%)
Air Algerie: 49,914 (8.83%)
Air France: 48,568 (8.59%)
Turkish: 40,044 (7.08%)
Tunisair: 34,067 (6.02%)
Ryanair: 29,673 (5.25%) – all the flights to/from Morocco
Egyptair: 22,317 (3.95%)
Aigle Azur: 22,146 (3.92%) – North Africa
British Airways: 19,940 (3.53%)
Jetairfly: 18,040 (3.19%)
Source: OAG.