The Indo-European languages spread into western Europe from the east. This linguistic movement was not necessarily coupled with the movement of peoples although this is perhaps the most likely mechanism.
Although historically, the Celtic, Germanic, Italic, Slavic, Hellenic and Baltic families are attested, the presence of Indo-European words in areas that were not affected by speakers of these language groups shows that they were not the first arrivals. Indo-European words occur in Sardinia, Corsica, Sicily and other parts of the Mediterranean littoral. One or more early declinations of proto Indo-European may have been very widespread. Lusitanian, found in central Portugal and adjacent regions of Spain, may be a survival of an early Indo-European derivative.
Throughout in western and central Europe, the varieties of Indo-European attested at the dawn of the historical period were preceded by earlier varieties of Indo-European that had diverged to a much lesser extent from the reconstructed forms of the proto Indo-European.
Elsewhere, the historically attested Indo-European languages were immediately preceded by non Indo-European languages.
This is easily seen to be the case in Anatolia where the recorded Indo-European languages all show strong traces of borrowing or inheritance from unknown non Indo-European predecessors. Greek has also retained traces of a non Indo-European substrate.