In fencing, but also in life, there is always a situation, justified or unjustified, where it is appropriate, desirable or necessary to apologize.
An apology should always be direct and sincere. For it to be effective and help both sides, it should consist of the following elements.
All these components should be meant seriously by you, otherwise they have little meaning. It is crucial that something changes in the situation, i.e. that your own behavior changes. Otherwise, apologies will be useless, and the anger will only increase.
Some of this can be expressed in very few words. Here are the good classics of fencing.
“Oh no, the hit was probably too hard. I didn't get the attack right and was distracted by another hit. I'm sorry. I'll be more careful in the future. Do you like cinnamon buns or beer? I'll bring you one later to make up for it. I apologize.”
Or even shorter:
“Oh no – I guess that hit was too hard. I messed up, that was stupid. I'll pay more attention there. A beer tonight to make up for it?”