  We present the first measurements of the projected clustering and intrinsic
alignments (IA) of galaxies observed by the Physics of the Accelerating
Universe Survey (PAUS). With photometry in 40 narrow optical passbands
($450\rm{nm}-850\rm{nm}$), the quality of photometric redshift estimation is
$\sigma_{z} \sim 0.01(1 + z)$ for galaxies in the $19\,\rm{deg}^{2}$
Canada-France-Hawaii Telescope Legacy Survey (CFHTLS) W3 field, allowing us to
measure the projected 3D clustering and IA for flux-limited, faint galaxies ($i
< 22.5$) out to $z\sim0.8$. To measure two-point statistics, we developed, and
tested with mock photometric redshift samples, `cloned' random galaxy
catalogues which can reproduce data selection functions in 3D and account for
photometric redshift errors. In our fiducial colour-split analysis, we made
robust null detections of IA for blue galaxies and tentative detections of
radial alignments for red galaxies ($\sim1-3\sigma$), over scales of
$0.1-18\,h^{-1}\rm{Mpc}$. The galaxy clustering correlation functions in the
PAUS samples are comparable to their counterparts in a spectroscopic population
from the Galaxy and Mass Assembly survey, modulo the impact of photometric
redshift uncertainty which tends to flatten the blue galaxy correlation
function, whilst steepening that of red galaxies. We investigate the
sensitivity of our correlation function measurements to choices in the random
catalogue creation and the galaxy pair-binning along the line of sight, in
preparation for an optimised analysis over the full PAUS area.
