A good rooster will protect all members of his flock, including protecting babies from other hens. Not all roosters are that good, though. I would not count on him protecting them. That is Mama's job.
That rooster may be confused as to what is happening, he may be worried that something is wrong with the broody, or he may be hanging around to protect her. In the wild, broodies are vulnerable while on the nest. I can't tell you why he is hanging around, but I would not consider it a reason to worry.
As JordanFamily said, it is usually the other hens that are the threat, but a good Mama will protect her chicks from any other chicken, hen or rooster. Again, not all Mama's are good. Some can be wimpy, but that is really pretty rare. Usually a broody hen has such a bad attitude that the other chickens, hens and roosters, very quickly learn to leave the babies alone. And it is very rare, but there have been reports on this forum of roosters taking over raising the chicks if Mama abandons them too early or a predator gets Mama. Very few roosters are this good.
I cannot guarantee you what will happen. They are living animals with different personalities and different levels of instincts. Bad things can happen, but I would trust a broody to take care of her babies until she proved otherwise.