But in ancient (or medieval) times the concept of a national border, with language A switching to language B when you cross it, was less of a phenomenon; standardised national languages are relatively recent in nature.I live 50 km away from the Czech border and have 0 idea of Czech grammar ... and I don't know anyone who has, either.
You might not be influenced by Czech directly, but at a village on the border people might be bilingual, and they might end up using Czech-like structures in German, and that could spread.
The 'have-perfect' structure is there in Hittite; I doubt it was an invention of Germanic languages that was calqued into Romance. However, it would also be a strange coincidence if languages in the same vague geographical region (cf. modern Greek as well) all simultaneously favoured a syntactic structure that is typologically quite rare. More likely, the seeds of this structure were present in both Germanic and Romance, but the fact that these language families were in close contact had a mutually-reinforcing effect that encouraged the prominence of the feature.