the italian language has no word for accountability, the closest is 'contabilita' which has no personal dimension, just accountancy really.
the other one...'notorieta' is fame, (for whatever reason), not notoriety, with its perjorative meaning.
fascinating what lexical and conceptual semantic equivocations live deep in the cracks between languages. ~"When an inner situation is not made conscious, it appears outside as fate." Karl Jung~
i have never heard your use of the phrase, perhaps it is currently only used in extremely formal italian. it rings somewhat archaic.
'ti rendi conto?' = 'do you grok that?'
your use may also be religious, as in final reckoning, in fact our word reckon seems rooted in the italian, via reconnaissance.
recognition is an interesting offshoot, when mere cognition insuffices, do it again! ~"When an inner situation is not made conscious, it appears outside as fate." Karl Jung~
Notoriété in French, adj notoire, means well-known - but this follows from the Latin notus "known". The English word notorious does have this meaning too, but has developed a strong pejorative streak. I think notorio in Spanish can have both senses too.
Comptabilité means "accountancy" in French. There is no single word for accountability. But the adj comptable is used to mean "accountable".
Tu te rends compte? Common FR expression meaning "Do you realize?". So rendre compte in everyday French means "to realize". But, in more formal usage, it does mean to account for (one's actions).
I'm not sure these differences are all that deep or significant, though.