I believe that Franck and Simon are in fact the same person and here's why.
The film is not in chronological order. Danny Boyle has stated this numerous times. Thus I believe the last scene of the film (Franck finding the I-Pad) is actually the first scene of the movie.
Franck and Elizabeth were together, and she was in fact a hypnotherapist, she leaves him and steals his painting (the Goya painting) as a reminder of the good that lies in Franck. When she makes the comment about how she thought the painting would remind her of "him" but instead it reminds her of Franck, the him in question is actually the violence inside Franck. Franck has two sides to him, and Simon is the violent and possessive personality within him.
Franck chooses to remove all memory of her, thus creating the events of the film.
The events of the movie attempt to make Franck come to terms with his inner violence and his obsessive nature.
This would help explain why certain scenes are looped (the delivery man, the use of the I-Pad, the soccer game) they are all events that Franck experienced prior to going into trance, thus they are fresh in his mind.
The woman that Simon murders is thus not real, but rather a way for Franck to visually see his own aggression. Franck's mind has to come to terms with whether he wants to keep his aggressive side (Simon) or let Elizabeth go, thus killing Simon.
The scene where Simon dies is that struggle. Only one of them can live. Elizabeth pushing Franck and Simon into the water is the death of Simon and the rebirth of Franck. The reason Elizabeth disappears when Franck resurfaces is because he has moved on and forgotten her.