The nonlinear Schrödinger equation describing weakly rotational wave packets in a fluid in the Lagrangian coordinates is derived. Rogue effects are possible in low-vorticity waves, and the effect of vorticity is manifested in a shift of the wave number in the carrier wave. Special attention is paid to Gouyon and Gerstner waves. It is shown that this equation in the Eulerian variables can be obtained from the Lagrangian solution with an ordinary change in the horizontal coordinates.