Here's a few reasons why a fusion of two or more languages don't occur in monolingual countries, like Belgium or Switzerland.

Let's start with Belgium and the example of Brussels. The city of Brussels is an enclave located in historic Flanders that was originally Flemish-speaking hundreds of years ago but rising immigration of French-speakers from Wallonia during industrialization in the 1800s together with the Belgian government preferring the use of French as the language of judiciary, administration, army, education, media, over Dutch (because Belgium gained its independence from Netherlands and wanted to distance itself, and French was also regarded as a more prestigious language at the time) made Brussels over 90 percent French-speaking today.

The Flemish speakers did not vanish and leave the city, rather they remained and were assimilated as French-speakers overtime. French was the language of the rising urban middle-class and the educated, and since both Flemish and French-speakers shared the same Belgian national identity, the Flemish speakers who became French-speakers did not regard this as a 'betrayal' of their culture. So there wasn't a fusion of the two languages in Brussels, it was one or the other, and the French there is the same French spoken in Wallonia which has a few Dutch loanwords but definitely nothing close to a language fusion.

So why does fusion of two languages rarely occur?

Much of this is due to geography. Historically mass immigration between different parts of monolingual countries does not occur, so since there was always a dominant group in one region, the dominant language was the one of the majority there.

Switzerland is a good example since it's so mountainous and the mountains were natural borders that isolated off parts of the country and throughout history made human movement difficult. That is why languages were well preserved in Switzerland and there's even a Romance language called Romansh spoken in the mountains in the south-east of the country. In Switzerland the French-speakers were concentrated around lake Geneva in the west and Italian-speakers resided in the mountain valleys in the south, so these became monolingual areas. Swiss people are more monolingual on average compared to Belgians.

But the mountains occasionally worked the other way in preservation and led to a blend of languages such as in the mountain village of Basse-Ville, Fribourg, where the locals developed a fusion of French and Swiss-German called the Bolze dialect. The town was located on the language border between French and Swiss-German regions. This was rare and only a few hundred locals spoke Bolze. Meanwhile the town of Fribourg, which was originally German-speaking, became French-speaking over the course of the 1800s due to immigration of French-speakers and industrialization. Today even German-speakers refer to the town by its French name of Fribourg, rather than Freiburg. So the Bolze fusion dialect evolved in a mountain village and didnt gain enough traction to be spoken in a big commercial town and today with media/information this type of isolation necessary for a language fusion is no longer possible. The population of a commercial city, like Fribourg, would prefer speaking a common language so trade and business could be made much easier with foreigners than if they had their own unique language spoken there.

One final consideration is that languages that are in two different families would rarely fuse together both grammar and vocabulary.

So for example other "mixed languages" like Petuh spoken in the border town of Flensburg, is a mix of Danish grammar and German vocabulary. Media Lengua in Ecuador is a mix of Spanish and Quechua but it only took Spanish vocabulary and lexicon (that accounts for 90 percent of vocab) while it kept Quechuan grammar and syntax. Tagdal spoken in Mali has a Songhai base grammar but majority Tuareg/Berber vocabulary. So in these cases the original speakers retained the grammar of their former language but adopted the entirely foreign imported vocabulary.

And regarding multilingual countries, the national identity of their people is not structured on the promotion of a single shared language, like in most modern nations, but rather on shared history, culture, etc. that is what unites them. Iran has many different languages but all its people identify as Iranian despite some of the linguistic differences. That's how multiple languages can coexist in a monolingual country.

I feel this is more a linguistic question than a historical one.

You may have heard of mixed languages or creoles, and they are indeed quite numerous. However, if you look at their distribution, you will notice a pattern: in almost all cases, these creoles arose as a direct result of colonialism. Thus creoles tend to be based on English, French, Spanish - all European languages. There is even a Japanese-based creole in Taiwan, part of Japan's colonial legacy.

This is not the only way language contact develops though. The first step in language contact, and most common by far, is lexical borrowing, or loanwords. Loanwords permeate the world's languages: English is a good example of this, because the loans in it outnumber directly inherited vocabulary by far. In some cases, more than just words get borrowed: phonemes (sound elements), morphemes (e.g. prefixes or suffixes), and grammatical structures can all be borrowed as well, though they normally do so through lexical borrowings. In areas of intense linguistic contact, it is common to see diffusion of features between several languages (often genetically unrelated ones). These areas are called Sprachbunds, and are an object of study.

I should note a very important detail here that people often overlook: language contact only happens as a consequence of multilingualism. It is not enough for two groups of people to live next to each other if they don't speak each other's languages. At least some people must learn enough of the other group's language to be able to talk with them, and these people serve as conduits for new ideas and words into their native group.

But back to your original question: why don't Belgians speak some version of Frutch? Well, that would depend on your definition of a mixed language. Truly equally mixed languages don't happen, because there is always an imbalance, be it in the number of speakers or their relative status. In the case of Belgium, French was its official language for a substantial period of time, and local Dutch varieties were supressed, leading in turn to resentment. Nevertheless, language contact did occur, but it was more prevalent in local dialects, which are no longer learned by young people as their native language. French influence is seen for example in the provinces of West Flanders and East Flanders, where local vocabulary has a lot more French loans than Standard Dutch. The "French R" pronunciation characteristic of the city of Ghent may also be due to French influence.

There are also cases of linguistic displacement, whereby a region's predominant language changes completely, often by force. This happened in Brussels, which used to be predominantly Dutch-speaking, but is now French-dominant. Such displacement can also be accompanied by substrate influence, whereby a language that is being replaced (the substrate) influences the language that is replacing it (the superstrate). Taiwan underwent a shift from being a majority Hokkien (Southern Min) speaking country to being a majority Mandarin-speaking one, within the span of just 1-2 generations; but this in turn changed the Mandarin spoken by Taiwanese people, infusing it with Southern Min features.

So to recap, there are many different kinds of language contact, from borrowing a few words, all the way to massive structural changes and creolization. Language contact occurs all the time, but more often in small ways that are imperceptible to the casual observer. Creolization is rarer, and requires special circumstances.