Wonderful story. It would be perfect if the slashiness wouldnt be there. I just dont see it with those two but no judgment from my side if you do. Its still a beautiful look behind Javerts eyes, his inner turmoil and the way he sees himself and those around him. I find it amazing how you convey all of this by letting them (mostly) talk about something else that isnt even about him. The very few times when it is about him, he pushes it aside so fast, its almost not there. And still its all about him. About his life, his feelings, his regrets and hopes, even while theyre talking about Cosette.
All the things they said sound real and (besides the reasoning you choose) I can imagine them have this conversation. And I love the hug at the end. Very touching, even when one (like me) chooses to ignore the slash.
btw: I like how you let him compare the garden to the stars, with its seasoning and order. Very much how he might see it.
Im really surprised this didnt get any reviews yet, but people tend to be lazy writing a review at all, so I dare to say it has nothing to do with the quality of the story. I enjoyed it very much. Hands down. Good work, my friend.