Should I denounce the professor for not avoiding a fight?

A few days ago, my son came home with his clothing torn and a big bruise in his arm. When I asked him what had happened, he told me that he had had a fight with another kid in the playground when they were coming out of the school. I was very upset because this was the first time that my son got involved in a fight, and by chance, when I was speaking with the mother of another kid, she told me that it had been a shame because there was a teacher near that had seen everything and had done nothing to stop the fight. Now I am thinking about reporting the teacher, for not having pulled them apart.

Could I take legal actions against him or the school?

Yes, as long as you can prove by any means that the school staff, like the teacher you mention, could mediate to stop the fight and did nothing, or took too much time to control the situation. In this case, if the mother you spoke with witnessed the incident and she is willing to give testimony, the proceeding will be easier.