The Narrator
The Narrator is not named, but he takes us through the film as he tells us of Davos' experience as a child at The Jetty. He is the bridge between the characters which are seen in a series of still photographs and the narrative the audience is following. And he is the one who breaks the news of Davos death in the end of the film.
Davos
Davos is the main character in the film. He has held on to a single moment from his past at The Jetty where he witnessed a chaotic event with a man running towards a woman who collapses before his eyes. He's now grown and become a test subject for time travel in a post-nuclear war France in 1962. He is able to travel to the future and the past, but upon his return he receives the news that he is sentenced to death as he is a convicted criminal. He convinces his jailers to allow him to go back in time instead of facing his fate in the present date, only to be killed at The Jetty in the same moment that's haunted him his entire life. He's witnessed his own death.
The Woman
The Woman from Davos' memory of The Jetty. He goes back in time to meet her as he believes she is the key to figuring out why this moment is so important to him. He falls for her and when he returns to the past he is running towards her when a hitman ends his life with a shot through his chest.
The Experimenter
The Experimenter is the lead scientist who creates time travel in 1962 France. He sends Davos to the past and the future in order to obtain help for saving the people of the present day. He simply uses Davos as a means to an end as Davos is killed rather than being rewarded for his service.