It might be in the original French, but it’s been anglicised and adopted as an English language term:

https://www.oed.com/dictionary/toot-sweet_adv?tl=true

I love this way English has of swallowing and digesting terms from other languages. https://www.oed.com/dictionary/the-tooter-the-sweeter_phr

Quelle surprise (wink wink)!

This is the first time I've ever seen "toot sweet" used. The more you learn :)

To be clear, it’s a jokey informal English language term, not a standard one.

There's also the UK practice of deliberately mangling French for comedic effect, as in Del Boy's cries of "Bain Marie!" and "chateuneuf-de-paper!" on 1980s TV. Saying "Toot sweet" can fit right into that bucket.