We used the Plateau de Bure Interferometer (PdBI) to map a sample of 15 submillimetre galaxies (SMGs) in the COSMOS field at the wavelength of 1.3 mm. The target SMGs were originally discovered in the James Clerk Maxwell Telescope (JCMT)/AzTEC 1.1 mm continuum survey at S/N_(1.1 mm) = 4−4.5. This paper presents, for the first time, interferometric millimetre-wavelength observations of these sources. The angular resolution of our observations, ~1."8, allowed us to accurately determine the positions of the target SMGs. Using a detection threshold of S/N_(1.3 mm)> 4.5 regardless of multiwavelength counterpart association, and 4 <S/N_(1.3 mm) ≤ 4.5 if a multiwavelength counterpart within 1."5 is also present, the total number of detections in our survey is 22. The most significant PdBI detection of S/N_(1.3 mm) = 10.3 is towards AzTEC19. Three of our detected SMGs (AzTEC21, 27, and 28; which corresponds to 20%) are marginally resolved at our angular resolution, and these sources are found to have elongated or clumpy morphologies and/or multiple components. Using optical to near-infrared photometric redshifts, available spectroscopic redshifts, and redshifts estimated from the radio-to-submm spectral index we infer a median redshift of z = 3.20 ± 0.25 for our sample. To study the overall multiplicity and redshift distribution of flux-limited samples of SMGs we combined these sources with the 15 brightest JCMT/AzTEC SMGs detected at 1.1 mm, AzTEC1−15, and studied previously. This constitutes a complete, flux- and S/N-limited 1.1-mm selected sample. We find that the median redshift for the 15 brightest JCMT/AzTEC SMGs (z = 3.05 ± 0.44) is consistent with that for AzTEC16−30. This conforms to recent observational findings that SMGs do not exhibit any significant trend between the redshift and (sub)mm flux density. For the combined AzTEC1−30 sample we derive a median redshift of z = 3.17 ± 0.27, consistent with previous results based on mm-selected samples. We further infer that within the combined AzTEC1−30 sample ~25 ± 9% of sources separate into multiple components.