You have to apologise. Say it properly.
Work out what actually happened, what it cost them, and the one thing you will do next — then a message they can accept.
Who is this going to, and what is the relationship?
An apology has four parts
What you did, what it cost them, what you are not going to explain away, and what happens next.
Apologising to a client
The version that protects the relationship without admitting liability you do not have.
Apologising to someone close
When the message has to be short, and when it has to be a conversation instead.
Questions people ask first
German and French versions?
Yes — the same pack, with the local register: German apologies are more formal, French ones shorter.
Should I apologise in writing or in person?
The pack asks which, and writes for that channel.