The notion that patterns of linguistic and biological variation may cast light on each other and on population histories dates back to Darwin's times; yet, turning this intuition into a proper research program has met with serious methodological difficulties, especially affecting language comparisons. This article takes advantage of two new tools of comparative linguistics: a refined list of Indo-European cognate words, and a novel method of language comparison estimating linguistic diversity from a universal inventory of grammatical polymorphisms, and hence enabling comparison even across different families. We corroborated the method and used it to compare patterns of linguistic and genomic variation in Europe.