Since you don't particularly care about the timeframe, one interesting case to consider is the Balkans. Albanian, Eastern Romance, Greek and Slavic coexisted there after the seventh century AD, roughly (with Eastern Romance a newcomer compared to Albanian and Greek, and Slavic even newer still). The Roms (and Roma) showed up around the 12th century, and the Ottomans entered the picture in the 14th century, and brought Turkish with them. In the late 15th/early 16th centuries, Judeo-Spanish showed up. This has resulted in what we call the Balkan sprachbund, where many languages from different families show striking similarities as the result of contact.

The speakers of these languages clearly participated in a rather extensive amount of linguistic contact. While the historical situation is muddled by population transfers/ethnic cleansing/genocide in the 20th century, the linguistic record of contact is obvious. For instance, Bulgarian, Greek, Macedonian, and Romanian all have greatly reduced nominal declensions compared to older forms. Albanian, Bulgarian, Greek, Macedonian, and Romanian all have innovated definite articles--in every case but Greek, these are post-positive (so Macedonian čovek ~ čovek-ot 'a person' ~'the person', with parallel examples in all the other languages). The list of these examples can go on indefinitely, and covers basically every level of linguistic structure, from phonetics to syntax.

So what does this tell us about multilingualism in the Balkans in the Ottoman period? Well, the way things fall out, we can distinguish more and less central members of the sprachbund. More central members exhibit more examples of convergence. According to Victor Friedman, Macedonian is the most central member. Albanian, Bulgarian, and Aromanian are on the next level out. Greek and Romanian are less central yet, and after that come Roma, Judeo-Spanish, and Balkan Turkish, which for various reasons are the least convergent. Macedonian, which is geographically most central, shows the largest number of shared features with other members of the sprachbund. On the peripheries, we have languages which were either very prestigious (e.g. Turkish, associated with the state) or not prestigious at all (e.g. Roma, who were shunned by many communities and generally lived separately).

If you're interested in reading more about this, there's a ton of articles in English; you might look especially for stuff by Victor Friedman and Brian Joseph, who are both very concerned with patterns of multilingualism and contact.

Since you mentioned the Middle Ages, I'll add something toward the end of what is considered the medieval period. Most people know that William defeated Harold in 1066 (there is an extraordinarily detailed and contested argument as to the exact contenders to the throne. The issue, ironically, is about Edward the Confessors' issue. According to a number of chronicles, he was so pious as to abstain from any intercourse, thus producing no heirs-apparent. For a detailed, academic, and extraordinary influential book on the topic, which also pertains below, I'd recommend David Carpenter's The Struggle for Mastery: Britain, 1066-1284). Anyway, the Normans initially had limited control over their new territory. They themselves spoke Norman French which is very close to later medieval Latin, but found themselves in a land where people spoke Anglo-Saxon. The traces of which I should add are still found in our everyday speech. The people the Norman's encountered (with the exception of monastic centres) had no idea what was being communicated to them except by word of mouth and remained concentrated in their immediate proximity or, arguably, their hundred (an administrative district from which 100 men could be called upon to fight). I know this is about language, so here it is in this context: Norman French was the lingua franca until the later fourteenth century. Many people outside the immediate sphere of the king's control or his roving justices maintained a distinct dialect which eventually blended its Germanic roots with Norman French and Latin (why do you think we should never begin a sentence with a preposition? Because in Latin it is poor syntax and is often misleading). There are of course exceptions to this hegemonic language. Gaelic being the most obvious example of this, in its many and excellent variations. In short, to answer your question, the average person in the context of Britain spoke one language for a relatively short period of time.