They do have the late 18th-century Old French Sign Language as their common ancestor, but have diverged during the subsequent 200 years, so that mutual intelligibility between modern users has been greatly reduced.
The abbot Charles-Michel de l'Épée wanted to give them religious education, and thus learnt their language, after which he made some adjustments of it himself.
Educators from all over Europe came to this and later French schools for the deaf in order to adopt l'Épée's teaching method, and introduce it in their own countries.
In 1790, he founded the Henri Daniel Guyot Instituut [nl], the first Dutch school for the deaf, after the example of l'Épée, who he had visited in France.
In September 2019, D66, PvdA and CU proposed a bill of law initiative for official recognition of NGT.