This isn't a game for everyone. Rayman was an hardcore platformer that is still unfair.
Its controls are more suited for controllers (and if you have one, please use it) but the touch controls work.
We wrote a review for Rayman Classic when it came back on iOS and we were quite pleased with the port. It's not a remake (but I had to make the pun) but an exact copy of the game you remember from the jaguar era.