Maybe you could help him find out what makes his sleep better or worse. My husband has a pretty strong reaction to caffeine. It gave him hypervigilance and nightmares. Unfortunately he was addicted to it. Support him to drop habits like this if he has one.
Some people have bad reactions to eating too much in the evening, not working out enough, working out too much in the evening.
There are some scents which are recommended for sleeplessness and nightmares such as orange peel. Even if it does no help he knows you care.
I think you might not always be able to help him but you will be able to show him you are there and that he is not alone. Knowing someone cares about them is sometimes the best medicine for our guys. If he is not feeling fit because he did not sleep much, show him you don't care and think he is cool anyway, tell him how much you like being around him, maybe help him with one of his chores.
Some guys do not want their woman to worry about them. They just want to be strong for them. In that case it is good not to make to much of a fuss. So while showing him you are always there for him do not go "OMG, poor spouse, that must be horrible. Oh, I must safe you". Not saying that you are doing this. Not sure if your guy is one of that guys.