This is where Europe and US are a bit different. For the longest time (until the mid 1960's or so?) semi-autos were generally illegal in most of Europe, and to this day they are still shunned and frowned upon by the older/more traditional generation, although I understand that this is the fastest growing hunting rifles market segment nowadays, albeit in specifically non-military looking form. They are apparently considered the cheaper alternative to European doubles for driven wild boar hunts.
This is only partially true. Pls allow me to clarify from local European perspective.
Semi autos are banned in countries like UK, Netherland, Norway.
They are not banned in other countries: Italy, Slovenia, Croatia, Check republic, etc
Member states of EU are generally obliged to follow European firearms directive in their own national legistlative. The directive does not ban semi-autos, but member states may impose stricter rules.
Recently, there was very strong initiative from EC (European commision) to ban all semi auto rifles for civilian use, but finally the bill did not pass on that point. So, semi autos remain as legal in some countries on European continent, in most cases with limited magazine capacity.
If I am not mistaken, rifles are limited to 10 rounds per mag by directive, or less if so regulated by member state.
Europe has very good - real hunting, traditional looking, semi auto rifle production on the market, and the rifles are being sold.
I think the most popular are: Benelli ARGO (sold in US as R1), and Browning BAR (in several versions), followed by few others: Sauer 303, Heanel SLB, Heckler and Koch 770, etc. There will be others, but this is what first comes in mind.
As mentioned, they are very good substitute for more expensive double rifle with primary use in driven boar hunts, and only secondary as general purpose hunting rifle.
Most popular calibers of semi auto hunting rifle offered are: 308 win, 30-06, 9.3x62, and very interestingly 300 win mag (for which I really do not see the need in shorter barrel semi autos, and for shorter ranges in driven hunts, but it is available any how)
AR15 platform on the hunting market is not popular in EU, (although present), partly beacuse of long hunting (and rigid) tradition, and general view of how hunting rifles shold look like.
All four (hunting) rifles I mentioned, look really, as hunting rifles.
Tactical look of ar15, generally is not appreciated in hunting community.
So, the black rifles, in Europe find their market in relativelly small practical shooting community (three gun shooting, or similar), but not in hunting community.
Other semiautos ex-mil, mostly used for collections, or local tournamets in old-fashion competition shooting, or plinking at the range are SKS, Yugo SKS, m76 (Yugo version similar to Dragunov), etc... But these are in small numbers.
Generally, semi-auto hunting rifles (Benneli, Browning, Sauer, Haenel, H&K) are present in good numbers, and even appreciated where legal. For hunting, most likely the regulation will be limit for 2 round magazine + 1 in chamber).
For sporting purpose, I think limit is 10 round mag as per latest EU directive, but this to be checked, as I am not 100% certain.
Any way, this is present situation in EU today, on this subject.
My impression is that community of this forum, obviosuly engaged in African hunting, and African hunt is traditon with taste, may find interest of such modern semi autos with taditional look (although not for African safari). Off all of those, my choice would be benelli, as it is easy to strip for maintenance, and has possiblity of changing the barrels. But I am not sayig others are not good. O, please take a look at Sauer 303... Its a beauty!