Mindset: bilingual or monolingual in TL?

tl;dr when learning a new language, do you conceptualize it as building a separate structure from your L1? Or do you integrate your TL side-by-side? What has worked for you?

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I had a conversation with a my speaking tutor who is a bilingual EN / FR translator. I mentioned to her that I was struggling with getting my brain to stay in French mode.

Her response is that I shouldn’t be thinking about the two languages existing separately in my brain or in my environment. She mentioned that there are leading scholars who no longer support the theories that different languages exist in different maps within the brain. So she encouraged me to think of my entire environment has been bilingual and that I could draw from either language at any time.

Unfortunately, that’s not my practical reality because very few people in my environment speak French. So, I couldn’t really switch in the workplace or even at home.

I’m trying to figure out how to hold both languages in my mind at all times, but it seems easier to me to have a French side and an English side. Partly because my English is far stronger than my French, I would really like to build an independently functional base for French.

I’m curious to know what has worked for others and if the “bilingual mindset” is a real language learning thing.