We all know about the political, sometimes continent-spanning marriages held together by a tight web of alliances. This makes me wonder, how would a German noblewoman be expected to interact with, say, her new Irish husband? I'm assuming Gaelic wouldn't be part of her education, so did she just learn the language over-time post-marriage? Would the husband learn her language, instead? Did she have an on-call translator?
Medieval Europe was a bit of a patchwork of different languages and dialects, and the lack of codified grammar and relative non-movement of population meant that regional variation in languages was also widespread. One amusing example of this is when a French force under Jacques de St-Pol was attacked during the night by a force of Flemish who used "Schild et de Vrient" (shield and friend), a phrase which the French could not pronounce, as a password. Any man who could not say it would be killed.
However, there were certain more widely spoken languages. Latin was the international language of the church and of scholars, and all liturgical books and scholarly documents would be written in Latin, and thus any educated person across the continent would be able to read them. French was similarly used in some places as a language of administration. In Medieval Flanders, for example, administrative documents were recorded in French or a strange mix of French and Dutch. Most of the nobility would learn either Latin or French, or indeed both, as a child and would thus be able to communicate with other nobles from across the continent. Charles V famously boasted that: 'I speak Spanish to God, Italian to women, French to men and German to my horse', implying a mastery of multiple tongues. Indeed, in some cases the noble in question would not have a 'native' tongue.
I'm probably best qualified to speak about England, where the relationship of the post Norman-conquest English nobility with the English tongue can best be described as dysfunctional. Most English nobles would speak anglo-norman, a dialect of French, as opposed to the english spoken by the lower classes. Indeed, Richard the Lionheart is alleged to have been unable to competently communicate in English. In any case, any well educated European noblewoman would have been able to communicate in French or Latin (although Latin was mostly used for written communication and records) with most other nobles across Europe, although she would need to adjust to the regional dialect. In the unlikely case that there was no common language between the two, there would certainly be other people in the court such as priests or emissaries who could assist in communication.
Further reading:
Nottingham University, Languages used in Medieval Documents
Malcolm Vale, Language, Politics and Society: The Uses of the Vernacular in the Later Middle Ages, The English Historical Review.