Multireference configuration interaction with singles and doubles (MR-CISD) calculations has been performed for the optimization of conical intersections and stationary points on the fluoroethylene excited-state energy surfaces. For the planar ground state geometry, the vertical spectrum including 3s and 3p Rydberg states was calculated. From this geometry, a rigid torsion around the CC bond strongly reduces the energy gap between So and Si states. Furthermore, a search for the minimum of the crossing seam shows that there exists a conical intersection close to the twisted structure and two additional ones for cis and trans pyramidalized structures. These three intersections are connected by the same seam. We have shown that the Hula-Twist process is an alternative way to the direct CC twisting in order to reach this part of the seam. Other conical intersections were also located in the CH3CF and CH2FCH, H-migration, and C3v structures. The photodynamics of the system is discussed based on topological features of these intersections.