"Chattes" is for female cats. Since in french, Masculine always win (figure of speech naturally), you have to say "six chats" because you don't know how many are males. The only case it would be correct : if you know for sure that all six cats are females.
Sooo doggie heaven exists Plenty of cats to chase around hot owner big mansion ...
In a show called Tiny House Nation, there was a family with the opposite - they had six dogs and one cat :P