Europe didn't have Smilodon, but it did have it's own types of sabertooths... however, most of them didn't make it 10,000 BC. The only ones that might have were Homotherium. However, from what I saw in the trailer, the big cat is undoubtedly a Smilodon, so it's way out of place.
and the movie is definitely AH (or maybe undiscovered history), what with the megalithic culture 10,000 years ago...