For some reason, HTC or Verizon decided to exclude FM radio from the Verizon HTC One, unlike all of its carrier variants (except for the Play Edition). Interestingly, the Broadcom FM / combo chip is the same as the one used in One Play edition. In other words, FM is disabled on it.
Even if you root it and install a FM app such as this one, all you will hear is static and you will not be able to tune into any of the radio stations.