Integrated Sensing and Communication (ISAC) systems face stringent hardware constraints, particularly regarding the high Peak-to-Average Power Ratio (PAPR) of standard OFDM, which necessitates power amplifier (PA) back-off and reduces sensing range. This paper investigates Frequency Modulated OFDM (FM-OFDM) as a constant-envelope solution capable of operating in the PA saturation region, thereby maximizing output power without the non-linear distortion penalties typical of conventional waveforms. We derive a comprehensive analytical framework for FM-OFDM in doubly dispersive channels, explicitly quantifying the inter-carrier interference (ICI) dynamics and effective channel gains in the discriminator domain. To address the unique phase structure of the waveform, we propose a tailored sensing receiver architecture utilizing slow time phase differencing for robust velocity estimation. Unlike prior works, we evaluate performance under a strictly normalized bandwidth constraint (B99), ensuring a fair comparison against CP-OFDM and Constant-Envelope OFDM (CE-OFDM). Simulation results demonstrate that FM-OFDM maintains superior detection accuracy and low BER even under fully saturated PA conditions and high Doppler shifts, validating its suitability for hardware-constrained ISAC transceivers.