At the moment, not much is known about how Ubisoft plans to take the side-screen platformer and port it to mobile devices. Fiesta Run and Jungle Run are both endless runners, a game type that's well adapted for mobile controls, but the original Rayman was a side-scrolling platformer.
A proper remake, which would maintain the playing style of the original game, would require into gamepad-like touch controls. However, given the complexity of Rayman's correct movements, the virtual D-Pad approach could translate in major headaches if not perfectly implemented. For this reason, we shouldn't exclude the chance that Ubisoft has transformed the original game in an endless runner, in line with the previous two mobile titles.
The original Rayman, launched in 1995 on the Atari Jaguar and the original Sony Playstation, is a gold standard for platformer games. For the mobile port, we certainly expect to Ubisoft to launch the game with remade (higher-res) graphics.