  A $^{59}$Co nuclear quadrupole resonance (NQR) was performed on a
single-crystalline ferromagnetic (FM) superconductor UCoGe under pressure. The
FM phase vanished at a critical pressure $P_c$, and the NQR spectrum just below
$P_c$ showed phase separation of the FM and paramagnetic (PM) phases below
Curie temperature $T_{\textrm{Curie}}$, suggesting first-order FM quantum phase
transition (QPT). We found that the internal field was absent above $P_c$, but
the superconductivity is almost unchanged. This result suggests the existence
of the nonunitary to unitary transition of the superconductivity around $P_c$.
Nuclear spin-lattice relaxation rate $1/T_1$ showed the FM critical
fluctuations around $P_c$, which persist above $P_c$ and are clearly related to
superconductivity in the PM phase. This FM QPT is understood to be a weak first
order with critical fluctuations. $1/T_1$ sharply decreased in the
superconducting (SC) state above $P_c$ with a single component, in contrast to
the two-component $1/T_1$ in the FM SC state, indicating that the inhomogeneous
SC state is a characteristic feature of the FM SC state in UCoGe.
