  We propose and analyze a mesoscopic Josephson junction consisting of two
ferromagnetic insulator-superconductors (FI-Ss) coupled through a normal metal
(N) layer. The Josephson current of the junction is non-trivially affected by
the spin-splitting field induced by the FIs in the two superconductors. In
particular, it shows sizeable enhancement by increasing the amplitude of the
exchange field ($h_{ex}$) and displays a switchable current-phase relation
which depends on the relative orientation of $h_{ex}$ in the FIs. In a
realistic EuS/Al-based setup this junction can be exploited as a
high-resolution threshold sensor for the magnetic field as well as an on-demand
tunable kinetic inductor.
