Fast Fourier Transform (FFT) is a key digital signal processing algorithm that is widely deployed in mobile and portable devices. Recently, with the popularity of human perception related tasks, it is noted that the requirements of full precision and exactness are not always necessary for FFT computation. We propose a top-down approximate Floating-Point FFT design methodology to fully exploit the error-tolerance nature of the FFT algorithm. An efficient error modeling of the configurable approximate multiplier is proposed to link the multiplier approximation to the FFT algorithm precision. Then an approximation optimization flow is formulated to maximize the energy efficiency. Experimental results show that the proposed approximate FFT can achieve up to 52% Area-Delay-Product improvement and 23% energy saving when compared to the exact FFT. The proposed approximate FFT is also found to cover almost 2× wider precision range with higher energy efficiency in comparison with the prior state-of-the-art approximate FFT.