Is cats a proper noun

No, 'cat' is a common noun, a Word for any cat of any kind.

A proper noun is the name of a person, a place, a thing, or a title; for example:

• Cat Deeley, host of TV series 'So You Think You Can Dance'
• Cat Island, The Bahamas
• Cat Fancy Magazine
• 'The Cat in the Hat' by Dr. Seuss