English has thousands of phrases which rely very much on the context. "Quite often" is one of those phrases in English that can be used to subtly reprimand someone or to complain without sounding too negative etc.
So although it normally means "Fairly regularly" it can also be used in a sentence such as "I don't mean to complain, but you do make this mistake quite often" which actually translates as "You're really getting on my nerves now- you make the same mistake all the time!" In fact we do this with any phrase using "quite"- someone in a loud pub might say "It's quite noisy in here" which generally means it's louder than a football stadium. "He's quite rude" means he's an absolute pig. Etc
Especially in the UK, where complaining in public is still regarded as a social minefield.
But in normal circumstances it usually just means "more than average". So "quite often" usually means "it happens more frequently [than other unspecified events]". So "I see my brother quite often" can mean "I see my brother more than I see other members of my family".
It completely depends on the context of the rest of the sentence or conversation.
Sometimes he took his dog with him when he felt lonely and quite often he first popped into a bistro to set himself up for a day.
It's a little vague, so I don't know whether that means "on the occasions when he took his dog with him, he often popped into a bistro first (before taking the dog for a walk)", or whether "he sometimes took his dog with him - but rather more often he used to pop into a bistro first (before doing something else).
In this context I'd say that "quite often" is more often than "sometimes", but less often than "very often.