  There are only five radio-loud quasars currently known within 1 Gyr from the
Big Bang ($z>6$) and the properties of their host galaxies have not been
explored in detail. We present a NOrthern Extended Millimeter Array (NOEMA)
survey of [CII] (158 $\mu$m) and underlying continuum emission of four $z>6$
radio-loud quasars, revealing their diverse properties. J0309+2717 ($z=6.10$)
has a bright [CII] line and underlying continuum, implying a starburst with a
star-formation rate SFR=$340-1200$ $M_\odot$ yr$^{-1}$. J1429+5447 ($z=6.18$)
has a SFR=$520-870$ $M_{\odot}$yr$^{-1}$ and its [CII] profile is consistent
with two Gaussians, which could be interpreted as a galaxy merger. J1427+3312
($z=6.12$) has a moderate SFR=$30-90$ $M_\odot$ yr$^{-1}$. Notably, this is a
broad absorption line quasar and we searched for the presence of high-velocity
outflows in the host galaxy. Although the NOEMA data reveal a tentative broad
component of the [CII] line as wide as $\sim$1400~km~s$^{-1}$, the sensitivity
of our current data is not sufficient to confirm it. Finally, P172+18
($z=6.82$) is undetected in both [CII] and continuum, implying a SFR$<22-40$
$M_{\odot}$yr$^{-1}$. The broad range of SFRs is similar to what is observed in
radio-quiet quasars at similar redshifts. If radio jets do not significantly
contribute to both [CII] and IR luminosities, this suggest no feedback from the
jet on the star formation in the host galaxy.
