Here in Canada, many children grow up in bilingual households. How do their developing brains learn to understand that while 'Hello' and 'Bonjour' mean the same thing, they can only be used within another set of words? Is this a problem? Are there 4 year-olds speaking with a mix of 2 different vocabularies?
The brain categorizes synonyms as being the same, no matter what the language but uses them according to context. In other words it ddoesn't hear Bonjour being used daily in one place, so doesn't utilize it there but the equivalent appropriate word according to time and place. As an analogy, you may have electrical tools in the garage (mind) but a plumbing crisis will lead to you looking for spanners etc. that are more useful for that task. It is also like manners you've learned as a child - given the correct setting, you automatically wheel them out but where it wouldn't be acceptable, you suppress such responses to fit in, unless you want to rebel deliberately (youth) or have lost the censorship mechanism (dementia), necessary to act in a way deemed correct to the situation. Memory and its selection is what makes society run as smoothly (or not as) it does: A butterfly chrysalis is the mind rearranging such data, to create a new answer.
As a South African I grew up bilingual, much as my parents and my children did. It was largely a painless process. Other South Africans are out and out impressive polyglots, able to make themselves understood in a five or six languages, not necessarily closely linguistically related.
The problem of mixing up languages certainly is genuine, but it is minute compared to what one might reasonably have expected. Language teachers at schools in South Africa and no doubt in Canada and Belgium are permanently on the alert for Anglicisms and other isms in every possible combination, they are regarded as serious solecisms, though in everyday use they are generally fairly harmless.
Or maybe not so harmless, in communities without formal teachers, isms form a major basis for the creation of new pigins, Creoles, and eventually new languages.In this connection a very useful book, and very pleasant reading, is: "The Language Instinct" by Stephen Pinker.
My daughter grew up bilingual in English and the Irish Language, by 8 she was quite fluent in both languages. It was interesting that although she could easily flip between the two languages, depending on how she was addressed, she found it very difficult to translate terms and phrases out of context of normal conversation.
For instance if she were asked "How would you say "this is my new hat" in Irish?", she would struggle, where as if someone asked her in Irish to describe what she had on her head, the response would be instant.
It suggested to me that the 2 sets of vocabulary and grammar systems were held in parallel in her mind, but it was not until she grew older (now 14) that she was able to connect and form links between them.