This paper presents a fractional generalized Cauchy process (FGCP) with an additive and a multiplicative Gaussian white noise for describing subordinated anomalous fluctuations. The FGCP displays intermittent dynamics on random time durations, whose analytical representation is given by the Ito[over ̂] stochastic integral. The associated probability density function is given by a generalized Cauchy distribution at the stationary state. A fractional Feynman-Kac formula is utilized to show that weak ergodicity breaking of the FGCP depends on the existence of the subordinator and/or the divergence of variance.