We report 250 GHz (1.2 mm) observations of a sample of 20 QSOs at redshifts 5.8<z<6.5 from the the Canada-France High-z Quasar Survey (CFHQS), using the Max-Planck Millimeter Bolometer (MAMBO) array at the IRAM 30-metre telescope. A rms sensitivity <~ 0.6 mJy was achieved for 65% of the sample, and <~ 1.0 mJy for 90%. Only one QSO, CFHQS J142952+544717, was robustly detected with S_250GHz = 3.46 +/-0.52 mJy. This indicates that one of the most powerful known starbursts at z~6 is associated with this radio loud QSO. On average, the other CFHQS QSOs, which have a mean optical magnitude fainter than previously studied SDSS samples of z~6 QSOs, have a mean 1.2 mm flux density <S_250GHz> = 0.41 +/-0.14 mJy; such a 2.9-sigma average detection is hardly meaningful. It would correspond to <L_FIR> ~ 0.94+/-0.32 10^12 Lo, and an average star formation rate of a few 100s Mo/yr, depending on the IMF and a possible AGN contribution to <L_FIR>. This is consistent with previous findings of Wang et al. (2011) on the far-infrared emission of z~6 QSOs and extends them toward optically fainter sources.
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