The first question is whether or not Cro-Magnon, or the early modern people who migrated into Europe, and Neanderthal people could actually mate and produce healthy, viable offspring. We may not know the answer to that for a long time (if ever). If they could mate, then I would find it hard to believe that they did not, given that the two groups overlapped each other in time and geography. That would explain why certain Neanderthal-like traits still persist in the European gene pool.
Such as?