||Topological semimetals with a nodal line is a class of topological matter extending the concept of topological matter beyond topological insulators and Weyl/Dirac semimetals. Here we show theoretically that a Floquet topological semimetal with a helical nodal line can be generated in 2+1 dimensions by irradiating graphene or the surface of a topological insulator with circularly polarized light. The helical nodal line is the nodal line running across the Brillouin zone with helical winding. Specifically, it is shown that the dynamics of irradiated graphene is described by the time Stark Hamiltonian, which can host a Floquet topological insulator and a weakly driven Floquet topological semimetal with a helical nodal line in the high and low frequency limits, respectively. One of the most striking features of the Floquet topological semimetal at low frequency is that the Berry phase accumulated along the time direction, also known as the Zak phase, has a topological discontinuity of pi across the projected helical nodal line. It is predicted that such a topological discontinuity of the Berry phase manifests itself as the topological discontinuity of the Floquet states. At intermediate frequency, this topological discontinuity can create an interesting change of patterns in the quasienergy dispersion of the Floquet states.