Abstract We present Atacama Large Millimetre/submillimiter Array (ALMA) high sensitivity ($σ _\mathrm{ P} ≃ 0.4\,$ mJy) polarimetric observations at $97.5\,$ GHz (Band 3) of a complete sample of 32 extragalactic radio sources drawn from the faint Planck–ATCA Co-eval Observations (PACO) sample (b < −75°, compact sources brighter than $200\,$ mJy at $20\,$ GHz). We achieved a detection rate of $~97\, {\rm per\, cent}$ at $3\, σ$ (only 1 non-detection). We complement these observations with new Australia Telescope Compact Array (ATCA) data between 2.1 and $35\,$GHz obtained within a few months and with data published in earlier papers from our collaboration. Adding the co-eval GaLactic and Extragalactic All-sky Murchison widefield array (GLEAM) survey detections between $70\,$ and $230\,$ MHz for our sources, we present spectra over more than 3 decades in frequency in total intensity and over about 1.7 decades in polarization. The spectra of our sources are smooth over the whole frequency range, with no sign of dust emission from the host galaxy at mm wavelengths or of a sharp high frequency decline due, for example, to electron ageing. We do however find indications of multiple emitting components and present a classification based on the number of detected components. We analyse the polarization fraction behaviour and distributions up to $97\,$ GHz for different source classes. Source counts in polarization are presented at $95\,$ GHz.