You can install ffmpeg-free from Fedora repositories and complement it with libavcodec-freeworld from RPM Fusion, i.e. dnf install ffmpeg-free libavcodec-freeworld.
Alternatively, you could try doing what dnf suggests, i.e. adding --allowerasing to the command. The ffmpeg package from RPM Fusion conflicts with the ffmpeg-free FFmpeg stack in Fedora, so the Fedora FFmpeg libraries need to be replaced with their RPM Fusion counterparts.