  We report on the first example of epitaxial Mn$_{3 + \delta}$Ge thin films
with a cubic $L1_2$ structure. The films are found to exhibit frustrated
ferromagnetism with an average magnetization corresponding to
0.98$~\pm~$0.06$~\mu_B$/Mn, far larger than the parasitic ferromagnetism in
hexagonal Mn$_3$Ge and the partially compensated ferrimagnetism in tetragonal
Mn$_3$Ge. The Hall conductivity is the largest reported for the kagome magnets
with a low temperature value of $\sigma_{xy} = 1587~$S/cm. Density functional
calculations predict that a chiral antiferromagnetic structure is lower in
energy than a ferromagnetic configuration in an ordered stoichiometric crystal.
However, chemical disorder driven by the excess Mn in our films explains why a
frustrated 120$^\circ$ spin structure is not observed. Comparisons between the
magnetization and the Hall resistivity indicate that a non-coplanar spin
structure contributes the Hall signal. Anisotropic magnetoresistance and planar
Hall effect with hysteresis up to 14 T provides further insights into this
material.
