  We report the results of a muon-spin rotation ($\mu$SR) experiment to
determine the superconducting ground state of the iron-based superconductor
CsCa$_2$Fe$_4$As$_4$F$_2$ with $T_{\rm c} \approx 28.3\,$K. This compound is
related to the fully-gapped superconductor CaCsFe$_4$As$_4$, but here the
Ca-containing spacer layer is replaced with one containing Ca$_2$F$_2$. The
temperature evolution of the penetration depth strongly suggests the presence
of line nodes and is best modelled by a system consisting of both an $s$- and a
$d$-wave gap. We also find a potentially magnetic phase which appears below
$\approx 10\,$K but does not appear to compete with the superconductivity. This
compound contains the largest alkali atom in this family of superconductors and
our results yield a value for the in-plane penetration depth of
$\lambda_{ab}(T=0)=423(5)\,$nm.
