I do not know which taxa you are interested in. May I suggest that you specify your question in this regard.
The global biodiversity information facility (http://www.gbif.org/) is always a good starting point. Otherwise check "species occurrence data at the diva-gis website http://www.diva-gis.org/Data
Brus, D.J., G.M. Hengeveld, D.J.J. Walvoort, P.W. Goedhart, A.H. Heidema, G.J. Nabuurs, K. Gunia, 2011. Statistical mapping of tree species over Europe. European Journal of Forest Research 131 (1): 145–157.
Hengeveld, G.M., G.J. Nabuurs, M. Didion, I. van den Wyngaert, A.P.P.M., Clerckx, M.J. Schelhaas, 2011. A forest management map of European forests. Ecology and Society. Special Issue Eforwood. In press.
Nabuurs, G.J., 2009. NFI plot level database gathered from 18 European countries. Digital database. Alterra and European Forest Institute.
Schuck, A., Van Brusselen, J., Päivinen, R., Häme, T., Kennedy, P., Folving, S., 2002. Compilation of a calibrated European forest map derived from NOAA-AVHRR data. EFI Technical Report 13, European Forest Institute.
Tröltzsch, K., Van Brusselen, J., Schuck, A., 2009. Spatial occurrence of major tree species groups in Europe derived from multiple data sources. Forest Ecology and Management 257 (1): 294-302.
Maps are available at: efi.int Data most probably upon request, I think!
The species you are looking for are well represented in National Forest Inventories (NFI). I don't know if a joint public database exists, but you may find the NFI datasets ready to download in their webpages (check http://efdac-catalog.jrc.ec.europa.eu/efdac_subthemes.jsp?DI=8) or even in the GBIF data portal (e.g. Spanish NFI, http://www.gbif.org/dataset/fab4c599-802a-4bfc-8a59-fc7515001bfa)
Maybe useful: there is a new tree species atlas of the JRC, and can (for now) be downloaded fully: http://forest.jrc.ec.europa.eu/european-atlas-of-forest-tree-species/