'Familiarities' sounds to me more like how a Victorian lady would describe inappropriate advances. I don't think 'familiarity' is normally plural in this kind of context in the modern day, and it doesn't make sense after only one remark anyway. Maybe it would work better when Vertraulichkeit is noncount, as an abstract quality.
'Refrain' also isn't normally used in spoken English, and it's not strong enough for this situation, where a judge would simply order the defendant not to do something.
In other contexts, describing it in the third person, you could say someone was over-familiar. But it wouldn't be a good idea to say that directly, because acknowledging his intent would show weakness -- and all the more so for a judge. Maybe you could get by with something like 'No personal remarks!'
But it's hard to imagine a defendant making such a remark in the first place, because everyone in the courtroom is instructed that they are allowed to speak only in answer to the lawyers' questions; no one typically gets to just make independent speeches. If a defendant did manage to digress, I think an American judge would be much tougher, more in control of the courtroom, because with a jury present, it's important for her to project authority. I would expect her either to ignore it as an irrelevant distraction, or to instruct him 'Just answer the question!', or if he persisted, to threaten him with contempt (of court).