The Science of Weather and the Nature of Science

The article itself mentions those. They are informal and descriptive;

He began to watch more carefully, and in this way, he became the first person to classify the clouds, producing a veritable cloud atlas for his first presentation to the Academy of Sciences in 1777. He divided clouds into five types: (1) veiled (en voile), (2) gathered (attroupés), (3) dappled (pommelés), (4) sweeping (en balayures), and (5) grouped (groupé).

https://en.wikipedia.org/wiki/Cloud#History_of_cloud_science says his nomenclature included 12 categories of clouds. Gemini AI gives you all their names.