We study the X-ray and optical properties of 16 broad absorption line (BAL) quasars detected in a ≈3 deg² region common to the wide synoptic (W-1) component of the Canada-France-Hawaii Telescope Legacy Survey (CFHTLS) and the XMM Large Scale Structure Survey (XMM-LSS). The BAL fraction is found to be 10 per cent in the full sample, 7 per cent for the optical colour-selected quasi-stellar objects (QSOs) and as high as 33 per cent if we consider QSOs selected from their infrared colours. The X-ray-detected non-BAL and BAL quasars have a mean observed X-ray-to-optical spectral slope (α_ox) of -1.47 ± 0.13 and -1.66 ± 0.17, respectively. We also find that the BAL QSOs have α_ox systematically smaller than what is expected from the relationship between optical luminosity and α_ox as derived from our sample. Based on this, we show, as already reported in the literature for quasars with high optical luminosities, that our new sample of BAL QSOs has X-ray luminosity a factor of 3 smaller than what has been found for non-BAL QSOs with similar optical luminosities. Comparison of hardness ratios of the BAL and non-BAL QSOs suggests a possible soft X-ray weakness of BAL QSOs. Combining our sample, of relatively fainter QSOs, with others from the literature we show that larger balnicity index (BI) and maximum velocity (V_max) of the C IV absorption are correlated with steeper X-ray-to-optical spectral index. We argue that this is most likely a consequence of the existence of a lower envelope in the distribution of BI (or V_max) values versus optical luminosity. Our results thus show that the previously known X-ray weakness of BAL QSOs extends to lower optical luminosities as well.