We define Hermitian $(ϵ,\delta )$-Freudenthal-Kantor triple systems and prove a structure theorem. We also give some examples of triple systems that are generalizations of the $u\left(N\right)\oplus u\left(M\right)$ and $sp\left(2N\right)\oplus u\left(1\right)$ Hermitian 3-algebras. We apply a $*$-generalized Jordan triple system to a field theory and obtain a Chern-Simons gauge theory. We find that the novel Higgs mechanism works, where the Chern-Simons gauge theory reduces to a Yang-Mills theory in a certain limit.