> The point is that "SIGN LANGUAGE" is idiomatic to the native speaker's tongue.

No, this is not true. French and French Sign Language are totally unrelated languages. Sign languages generally have little to do with the spoken language of the country they’re used in, that’s why for example American Sign Language and British sign language are completely different and not mutually intelligible despite the UK and the US speaking the same language (with only slight differences in accent and vocabulary).