Strongly correlated 4$f$- and 5$f$-electron systems often exhibit large effective masses due to cooperation between orbital hybridization and electron localization. In this context, the quadruple perovskite ruthenates $A$Cu${}_3$Ru${}_4$O${}_{12}$ have attracted considerable interest as rare example of heavy-fermion-like behavior arising from $d$-electron. However, the role of $A$-site cation substitution and its influence on the electronic structure remain unexplored. Here, we report a comprehensive study on the electronic properties of a newly synthesized CeCu${}_3$Ru${}_{3.25}$O${}_{12}$ sample, performing using synchrotron-based X-ray absorption spectroscopy (XAS) and photoemission spectroscopy (PES). By optimizing the Ru content under high-pressure synthesis conditions, we obtained a metallic compound exhibiting the highest electronic specific heat coefficient ($\gamma =$ 156 mJ/mol$\cdot$K${}^2$) within the $A$Cu${}_3$Ru${}_4$O${}_{12}$ family, together with a reduced effective magnetic moment (${\mu }_{eff}=$ 2.10 ${\mu }_B$/f.u.), indicating strong electronic correlations and substantial screening of local magnetic moments. The Ce $L_{III}$-edge XAS measurements revealed an intermediate valence state (Ce${}^{3.31+}$), indicative of 4$f^0$–4$f^1$ hybridization. A chemical shift observed in the Cu $K$-edge absorption suggests a modified Cu valence state, likely arising from indirect $f$–$d$ interactions mediated by oxygen ligands. The PES measurements uncover a peak at $|\omega |\sim$ 19 meV near the Fermi level whose energy and intensity show pronounced temperature dependence below 100 K, resembling the evolution of Kondo resonance peaks seen in $f$-electron systems. These findings suggest the coexistence of $f$–$d$ and $d$–$d$ hybridization at different crystallographic sites is likely an important factor for the enhanced $\gamma$, reduced ${\mu }_{eff}$, and Fermi-liquid behavior in CeCu${}_3$Ru${}_{3.25}$O${}_{12}$, offering a platform to explore correlated-electron phenomena in mixed-valent oxide systems.