The plural is 'furniture'
Is "furnitures" a real word, or just "furniture"? I would probably say "tables and chairs are items of furniture" or "types of furniture" or even just "are furniture".
Furniture is non-countable. Types or items are countable, as you suggest.
It is not a real word.
"Furnitures" doesn't exist
You cannot say 'furnitures' in English