Swiss Confederation has 4 official languages.

South African have 11 official languages in our 'matriek' everyone is expected to do at least two official languages, while some do three or four. There is off course people living there who where not educated there who cannot speak something else than English, but if you were educated in SA you are expected to do a first language and a second language.

White people often at the very least speak Afrikaans and English although French and German are not uncommon for person who have had a 'western' education, there still are German schools in most big cities.

Among the black communities English and Afrikaans is often spoken as a lingua franca but it is not uncommon for them to speak a number of what is typically considered 'African' languages.

There is off course one caveat and this is the Zulu's of Natal. Typically it has been considered practice that if you have anything to do with them you are expected to speak there language as they typically don't speak anything else, but even that is changing as the country keeps on becoming more western.

It is even not that uncommon for Natal's most selective public schools to teach Zulu as if you are entering any sort of trade in that province, as an adult it behooves you to learn it.

Native English speakers would tell you English is the language of the workplace, but if you live in big Afrikaner communities, which still exist in SA, you going to find Afrikaners seniors that are only begrudgingly going to speak English with you.

While this may not meet every specification of the question, in Cataluña, almost everyone is native in Catalá and Español. In Galicia, a majority in gallego and español. And in spite of years of suppression, there are still a sizable number of Basque speakers in “País Vasco.”

(But I was always amused that the Basque graffiti demanding independence and making only Basque official depended on words borrowed from Spanish)

PARAGUAY - Guaraní and Spanish

Note: before looking at this answer, readers might want to check my 'Notes on the Question' at the end of this post.

Most Paraguayans are mestizo, and Paraguay has a long history of bilingualism due to the fact that

the initial period of contact between the aboriginals and the Spanish was one of constant interaction. Collaboration between Indians and Spanish in Paraguay dated from the very beginning of Spanish colonization and continued through the initial years of Spanish occupation.

This 'collaboration' in the colonial period (mid 16th century to 1811) included a high proportion of mixed marriages:

One of the interesting aspects of Paraguayan social history is the frequency of mixed unions during the colonial period. Men greatly outnumbered women among European settlers, especially in the remote areas to the southeast of Bolivia, and an obvious solution to the problem was interethnic marriage. For much of the colonial era, then, the prototypical Paraguayan family consisted of a Spanish-speaking father and a Guaraní-speaking mother, a fact that may partly explain the widespread Spanish-Guaraní bilingualism that exists today in Paraguay.

Almost without exception in European colonialism, the colonizers language became that of the local elite while the bulk of the population stuck to indigenous languages. In Paraguay, though, this didn't happen:

As a result of an extremely limited immigration and the high percentage of mestizo households, a really insulated upper-class—differentiated by language, education, and economic status- did not develop in Paraguay. Unknown was the rigid association which developed in Peru between those in the elite and use of only Spanish.

Unlike almost all other native American languages, Guaraní did not just survive the spread of Spanish, it was adopted by Spanish settlers. From the time of independence in 1811, either Spanish or Guarani have been favoured at different times for different reasons, but never for long and never to the extent that one fell into a serious decline in usage.

Concrete evidence of bilingualism can be found in the Chaco War (1932–1935) when the military was instructed to use Guaraní and not Spanish on the battlefield. Such a change at literally the drop of a hat would not have been possible unless most of the soldiers at all levels were bilingual.

A 1960 survey of bilinguals in a rural area and an urban one threw up some interesting examples of how people switched from one language to the other depending on environment, mood and who they were talking to. Below are some situations and the language they were most likely to use in the city of Luque:

• With your parents - Guarani
• With your children - Spanish
• With your spouse daily - both
• With your spouse when angry - Guarani
• With your sweetheart - Spanish
• With the doctor - Spanish
• With the curandero - Guarani

Since 1950, a greater emphasis has been placed on Guaraní but, even so, the large majority of the population remain bilingual; 90% of the population speak Guaraní while 87% speak Paraguayan Spanish.

NOTES ON THE QUESTION

In view of criticisms of the question and some of the content in a couple of the answers, it seems a few points need emphasizing:

- First and foremost, the OP clearly specified the "bulk of the population" (i.e not the literate elite from whom the bulk of our evidence of past bilingualism stems).

- Second, the question also states "at near fluency". While it is undoubtedly true that most international traders (for example) were bilingual or even multilingual, it cannot be assumed from this that they spoke / understood at a level 'near fluency' (not to mention that they were a small percentage of the population). Nor can we assume that the (undoubted) existence multilingual regions meant that people had 'near fluency' and switched languages "as a matter of course".

- Third, a country having 2 or more 'official languages' is categorically not evidence by itself of bi- or multilingualism and thus barely seems worth mentioning. That said, Semaphore's examples of Gibraltar and Luxembourg look rock solid and the type of answers the OP is looking for.

- Fourth, LangLangC has rightly pointed to one weakness of the question; 'region' lets in, as LangLangC demonstrates, numerous examples of border regions. To be fair to the OP, this is a tough one when covering all historical periods (for why, see the final point).

- Finally, Brian Z has highlighted the other weakness; the inclusion of pre-modern societies (see his answer for details). Restricting the question to no earlier than c.1500 AD (or perhaps 1750 AD) would have helped.

Other source:

Donald F. Fogelquist, 'The Biligualism of Paraguay' in Hispania Vol. 33, No. 1 (Feb. 1950)

I want to make the case that this question is anachronistic in such a way that is is impossible to answer with a discrete list of cases. The idea of a country unified by a single language used both for official purposes and day-to-day conversation is itself very much a modern one. To a great extent, it was imposed from above by nation-building states over the last few centuries and didn't exist at all for most of human history.

As a result, many modern nation-states have more than one official language. Here is a list of 57 sovereign countries with at least 2 official languages. Certainly, in many if not all of these countries (and most of the others which are not included on this list), it is common for at least some groups of people within the country to use more than one language on a daily basis, and has been so for quite some time.

In pre-modern societies, where literacy was more limited and formal education effectively non-existent, language was dynamic and constantly changing. As a result, individuals bands, villages and regions all had different degrees of linguistic variation between them according to frequency of contact. This is why, for example, Papua New Guinea has over 800 recognized languages. While perhaps an extreme case due to the county's rugged terrain, it is illustrative of the point that far greater linguistic diversity would have prevailed in most of human history then we see in modern nation-states.

In sum, multiligualism is in many ways more historically "normal" than monoligualism.

Gibraltar

English is the official language in this British Overseas Territory, but the populace is also highly fluent in Spanish due to physical proximity and social interactions with its larger neighbour. In fact, bilingualism is so deeply entrenched, the population of Gibraltar routinely engage in code-switching in everyday speech.

That is, they switch between English and Spanish while speaking. The result is Llanito, which Wikipedia describes as "speakers appear to switch languages in mid-sentence".

Yanito (or Llanito) is the name popularly given to the native of Gibraltar as well as the local vernacular he/she speaks . . . Dating from the early or mid-nineteenth century, it came to be used to refer to the people of Gibraltar who, at that time, were predominantly Genoese.

_{Levey, David. Language Change and Variation in Gibraltar. John Benjamins Publishing, 2008.}

Given that Llanito emerged in the 19th century, we can surmise that Gibraltar must have already had a fully bilingual population by then. That is well before the deadline set by the question.

Luxembourg

Bilingualism has been enshrined in Luxembourg's basic laws since the Grand Duchy's first constitution, drafted in 1848. In fact, bilingual instruction were mandated shortly after the modern Luxembourg achieved de facto independence in 1839:

In accordance with the Education Act of 1843, basic literacy was taught via standard German, and standard French was taught as an additional language in primary school.

_{Kaplan, Robert B., Richard B. Baldauf Jr, and Nkonko Kamwangamalu, eds. Language Planning in Europe: Cyprus, Iceland and Luxembourg. Routledge, 2016.}

The net result of the commitment to bilingual (and later, trilingual) instruction is to create a trilingual populace:

Trausch . . . concludes that . . . 'from [the time of] the partition of 1839, the Luxembourgers became accustomed to using three languages in the course of their everyday life: their "native" Luxembourgish, German and French.'

Like Gibraltar, this everyday multilingualism become entrenched well before the Second World War.