Mainly you are right, but while Iberia had indeed contact with North Africa there where still many original european habitats. Europe as a continent exist since more than 500 million years.
It's different around, africa is in the moment coliding with europe, that's why we have active vulcanos in Italy and earth quakes in Turkey.
In fact the mediterranean sea open and closed a few times 6 million years ago.
They were once neighbors, but that was during the Perm when Pangaea was the only landmass.
When you want to know how the mediterranean sea would look like without water watch the documentary "the future is wild" on YouTube