Here's a website with a list of such textbooks for various languages:
https://vivariumnovum.it/risorse-didattiche/propria-formazio...
This is amazing, thank you!
In LLPSI's marketing materials, they call it the "natural method." (I've also seen "nature method.")
Another term is "comprehensible input" -- but I am not certain precisely how the two relate to each other. But hopefully they're enough for you to go on.
Re:Speaking Latin
by coyotespike on Tuesday September 14, 2021 @11:42AM
(#28526479)
Yes, the terms I've seen are "natural method", "comprehensible input", and "extensive reading."
The latter two refer more to a large volume of simple reading materials which let you work up on your own, practicing and slowly learning more grammar and vocabulary.
Re:Speaking Latin
by abecedarius on Tuesday September 14, 2021 @01:52PM
(#28528252)
For French I liked https://www.amazon.com/Mon-premier-dictionnaire-Roger-Pillet... which I picked up after some basic grounding with Duolingo. It's not a textbook but it is all in French yet for second-language learners.
(just checked archive.org, and sure enough, they've got a scan of the book I have, but it's a limited preview: https://archive.org/details/meinerstesbuch0000unse/mode/2up)