。
She wasn't fool enough to believe what he said.
Literal
She [topic-は] his [genitive-の] saying thing [object-を] believe [extent-ほど] fool was-not.
The ~ほど construction here is the 'extent' use: '(not foolish) to the extent of (believing what he said).' 信じるほど馬鹿 = 'fool enough to believe.' Negation gives the rebuttal: 'wasn't fool enough.' This pattern emphasizes the speaker's affirmation of the subject's intelligence by negating the threshold. 馬鹿 ('fool, idiot') is one of the most common Japanese insults — written in either kanji 馬鹿 or kana ばか/バカ.