  We used the Atacama Large Millimeter/submillimeter Array (ALMA) to map
$^{12}$CO($J$ = 1-0), $^{12}$CO($J$ = 2-1), $^{12}$CO($J$ = 3-2), $^{13}$CO($J$
= 2-1), and [CI]($^3P_1$-$^3P_0$) emission lines around the type 1 active
galactic nucleus (AGN) of NGC 7469 ($z = 0.0164$) at $\sim 100$ pc resolutions.
The CO lines are bright both in the circumnuclear disk (central $\sim 300$ pc)
and the surrounding starburst (SB) ring ($\sim 1$ kpc diameter), with two
bright peaks on either side of the AGN. By contrast, the [CI]($^3P_1$-$^3P_0$)
line is strongly peaked on the AGN. Consequently, the brightness temperature
ratio of [CI]($^3P_1$-$^3P_0$) to $^{13}$CO(2-1) is $\sim 20$ at the AGN, as
compared to $\sim 2$ in the SB ring. Our local thermodynamic equilibrium (LTE)
and non-LTE models indicate that the enhanced line ratios (or CI enhancement)
are due to an elevated C$^0$/CO abundance ratio ($\sim 3-10$) and temperature
($\sim 100-500$ K) around the AGN as compared to the SB ring (abundance ratio
$\sim 1$, temperature $\lesssim 100$ K), which accords with the picture of the
X-ray-dominated Region (XDR). Based on dynamical modelings, we also provide
CO(1-0)-to- and [CI]($^3P_1$-$^3P_0$)-to-molecular mass conversion factors at
the central $\sim 100$ pc of this AGN as $\alpha_{\rm CO} = 4.1$ and
$\alpha_{\rm CI} = 4.4~M_\odot$ (K km s$^{-1}$ pc$^2$)$^{-1}$, respectively.
Our results suggest that the CI enhancement is potentially a good marker of
AGNs that could be used in a new submillimeter diagnostic method toward dusty
environments.
