We present photometric redshifts (photo-z) for the deep wide fields of the Physics of the Accelerating Universe Survey (PAUS), covering an area of $\sim$50 deg$^{2}$, for $\sim$1.8 million objects up to $i_{\rm {AB}}\lt 23$. The PAUS deep wide fields overlap with the W1 and W3 fields from CFHTLenS and the G09 field from KiDS/GAMA. Photo-z are estimated using the 40 narrow bands (NB) of PAUS and the broad-bands (BB) of CFHTLenS and KiDS. We compute the redshifts with the SED template-fitting code BCNZ, with a modification in the calibration technique of the zero-point between the observed and the modelled fluxes, that removes any dependence on spectroscopic redshift samples. We enhance the redshift accuracy by introducing an additional photo-z estimate ($z_{\textrm {b}}$), obtained through the combination of the BCNZ and the BB-only photo-z. Comparing with spectroscopic redshift estimates ($z_{\textrm {s}}$), we obtain a $\sigma _{68} \simeq 0.020$ for all galaxies with $i_{\rm {AB}}\lt 23$ and a typical bias $|z_{\textrm {b}}\!-\!z_{\textrm {s}}|$ smaller than 0.01. For $z_{\textrm {b}} \sim (0.10\!-\!0.75)$, we find $\sigma _{68} \simeq (0.003\!-\!0.02)$, this is a factor of $10\!-\!2$ higher accuracy than the corresponding BB-only results. We obtain similar performance when we split the samples into red (passive) and blue (active) galaxies. We validate the redshift probability $p(z)$ obtained by BCNZ and compare its performance with that of $z_{\textrm {b}}$. These photo-z catalogues will facilitate important science cases, such as the study of galaxy clustering and intrinsic alignment at high redshifts ($z \lesssim 1$) and faint magnitudes.