The Inspector Edit
Smith and the Inspector seem to have a long father-son like relationship. Smith seems to be the only one who knows about the Inspector's past and what happened to his family. The Inspector also seems to trust him, but also see him as too young and open about his emotions. He truly believes that Smith is still just a "kid".
Smith shows admiration towards Éclair, probably due to her rank. He also shows a slight interest in her, which can be seen when he calls her "Éclair-chan" instead of "Éclair-san", which is the standard way of calling an another agent/policemen.
He also tells her about the Inspector's past, as he seems to be also more open towards Éclair. When he finishes the story, he makes two devil horns at his head to make Éclair smile, or even laugh after such a sad story; however, Éclair doesn't really gets happier.
Smith didn't show any signs of interest towards Lumiere. However, they seem to have a professional relationship, as they talked before getting onto the ship to transport the criminal Drake from Colce to Borgall.