I think it is likely that Europe was covered by the following language families during the Neolithic. There would have been some amount of overlap which is indicated by the blurred divisions. The second map has lines to provide a better idea of the areas covered.
http://img11.imageshack.us/img11/841...iesofneoli.jpg
http://img10.imageshack.us/img10/841...iesofneoli.jpg
These in turn would have partially displaced the earlier hunter-gatherer populations of Europe which likely belonged to the I haplogroup. If haplogroup I was indeed descended from IJ then it is likely that Europe's hunter gatherers spoke what is now termed 'Afro-Asiatic' in my opinion.
This was latter pushed back as Neolithic farmers replaced and assimilated the earlier cultures, with Afro-Asiatic being latter reinforced in some areas with farmers, metalworkers and traders travelling along the coasts (Megalithic culture). Basically it is Venneman's Vasconic theory whilst Finnic in NE Europe makes sense and fits the 'Finnic northern Europe theory' and South Caucasian is my own theory and ultimately I think Basque may be a distant relative of it.
South Caucasian should really be South or North Caucasian, either or maybe even both groups could have been present.