The ferromagnetic superconductor URhGe has been known to exhibit an extremely large enhancement of the upper critical field when the field is confined and rotated in the (ab) crystal plane. Our high-field Co-59 NMR measurements on 10% Co-doped URhGe up to 30 T prove that this unconventional behavior of the superconductivity (SC) is associated with a strong anisotropy of field-dependent quantum fluctuations near a tricritical point. These fluctuations are rapidly suppressed by the field component along the c axis, while being unaffected by any field component along the a axis. The observed close interplay between the SC and quantum fluctuations strongly supports a pairing mechanism mediated by these fluctuations in URhGe.