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If this question is answered in the game, I must have missed it. You learn a couple of things about Lermitage later in the game, but Prince James' men were looking for the baby not the treasure so I don't see how those things are relevant.

Curiously, you don't get points for matching the tire tracks from the car to the ones at Lermitage, although you do get points for matching the tire tracks at Chateau de Serras. I'm guessing it's because Chateau de Serras is where they were captured and killed but that doesn't explain why they went to Lermitage
Maybe the game designers just put those tire tracks there as a red herring? Make you think the killers lived in the cave at L'ermitage? If that's the case, it worked. the first time I played, I was absolutely certain the killers must live in the cave at L'ermitage.
Maybe I'm just slow, but this game does not give you any introduction to the plot whasoever, right?
i mean, the intro is just gabriel coming to in the train, and all of a sudden there's talk of vampires and a baby and stuff...maybe i'm just not catching on, but...what?
An introduction was given in a comic. You can read that here.
So Prince James thought Gabriel was capable of staying up all night every night? I guess he didn't realize that even the Schattenjager is human.