This is going to vary a bit from country to country, but I think on the whole, the answer is obviously yes. In most institutions in these countries, not only is teaching in the country's usual language, but so is the life of the department in most important respects. I spent 6 months in France as a visiting scholar at Paris 7, and had a fairly rudimentary command of French (enough to navigate life in France, but not good enough to carry on a conversation), and leaving aside teaching, most conversations in the department, and most academic talks were in French. In my situation, things were basically fine, but I could not have functioned as a staff member without improving my French very quickly.
France is something of a special case (though I suspect Spain, Italy, Poland, etc. would be similar). The Netherlands and Scandinavian countries are more used to expecting nobody speaks their language (and can expect greater English fluency from students), but even there, I'm sure knowing the language would be necessary for many positions, and a big advantage for the rest. If nothing else, it shows a commitment to being there which would be appreciated.
EDIT: You can also see examples of how this is dealt with by looking at job ads from the season that's winding down now (I'm going to use examples from MathJobs, since that's what I know; since that's a US-based site, it's going to be slanted toward ads looking to recruit English speakers). Some will make it clear that functioning in the local language is not a professional requirement or at least don't specify it is:
Some will specify that there is a transition period:
Some seem to expect that there already is language fluency:
That's actually more slanted toward English speakers than I expected, but of course, posting on MathJobs is a very biased sample, since it's mostly a North American site, and I think you only post there if you want recruit North Americans (that's including students or postdocs from abroad currently in North America). It's notable that from a lot of countries (Israel, for example) there are many postdoctoral positions on MathJobs that don't expect the ability to teach in Hebrew, but no permanent positions.