Luc is a French soldier with a massive head wound who dies in Briony's arms.
He's not just any soldier with a massive head wound, though. He's also, possibly, a symbol of Briony's husband, Thierry, who dies in 1997, two years before the last chapter of the book.
What evidence is there that Luc is Thierry? Well, both men seem to be French (the picture of Thierry was taken in Marseille, and Thierry is a French name). Also, Luc tells Briony in his delirium that he loves her, which prompts Briony to imagine "the unavailable future" in which she would have spent her life with him "loving her in his eager way" (3.218).
It also seems significant that when Briony looks at her husband's picture in the last part of the novel, she immediately thinks "One day I would be asking who he was" (4.23). She has vascular dementia, and shortly she will be detached from memory and the world, just as Luc was when she met him.
If Luc is her husband, and he dies in the novel before they could meet, you might see this as a kind of atonement. In one story, Robbie and Cecilia never get their love, while Briony and her husband get theirs. But when Briony retells the story, Robbie and Cecilia get together, and Briony's love affair is erased before it can begin.
Briony says she likes happy endings, but she's obviously got a thing for tear-jerkers as well.