The boars they eat in Astérix are Sus Scrofa. The pigs we eat nowadays are originally the same species, now slightly altered by domestication and selection. They are sometimes considered as a subspecies Sus Scrofa Domesticus, and sometimes their own species Sus Domesticus. In any case, they are very close to each other, and I am not sure the difference between a feral Sus Domesticus and a proper Sus Scrofa would be significant. They still can mate.

There were indeed plenty of boars in medieval Europe, and there still are plenty of them now.