Translation:I do not think that there are few cats in Europe.
Yeah, in the lesson notes somewhere it said 'Russian has consistent negation'. So you have sentences like Я никогда ничего не думаю.
Can anyone comment, does this rule also apply to мало and много? e.g. would you say 'I don't think there are not few cats' to mean 'I think there are many cats'?
It does not apply here, for two reasons. First, because мало is not considered a negative; second, because "что в Европе мало кошек" is a subordinate clause. Similarly "Я не думаю, что он ничего не знает." means "I do not think that he knows nothing." not "I do not think that he knows anything."
Some time ago I stumbled upon a discussion on the Internet about a group of supposed animal right activists who apparently transfered stray dogs to Germany, because, as they claimed, they have more chances to find a home in Germany then in Russia. Some people on that forum were very sceptical of the idea because they thought that Germany must've had enough if it's own dogs so they didn't need our strays. Those people speculated that all of that was a ruse to obtain animals for experiments. Change "dogs" for "cats" and you'd see how this sentence would be relevant in that discussion.