Fine. Suspend him, too.
There has to be a zero tolerance policy for fighting. It's their job. Do you know how much shit you'd be in if you punched a guy in the face at work? If the NFL wants to be a good role model, part of the community, appeal to families, etc., they can't have guys fighting.
It hurts their brand and is completely unacceptable.
I worked in a job that had somewhat harse work conditions and was very physical. As can be expected fuses got short and the company had a policy that no employees could get into a fight period, even off work, because some of us hated each other. It was the worst policy because cowardly little pussies would talk shit knowing no one could touch them.
If you are going to push another person's buttons in order to piss them off, you had better be willing to deal with the consequences.
No suspensions needed, just money. The people who need to be suspended are the players who continually lead with their helmets in order to blow the other player up.