In the interests of pedantry and general education of happy mutants I will quibble with your characterisation in some respects.
UK employment law - which even with Brexit we still have to count as European employment law - would work a little differently from what you describe…
Tedious wall of text
So far so good.
Bing! At this point, you have probably unfairly dismissed the employee. 
You first have to go through some sort of ‘fair procedure’.
Basically, write to him, tell him he is facing disciplinary proceedings that could lead to his dismissal because of allegations that on 23rd of whenever he masturbated into the mayonnaise, invite him to a disciplinary meeting, provide him with copies of the evidence and tell him that he has the right to be accompanied to the disciplinary meeting by a work colleague (“Erm, Janet? Would you accompany me to my disciplinary hearing. They say I was masturbating into the mayonnaise.” Enjoy the weird looks in the staff canteen 
) or a suitably trained trade union rep. (in the vanishingly small case that you are a union member).
Then you fire him.
And confirm it in writing and tell him he has the right to appeal (in writing). Again - meeting, colleague/trade union rep.
Then you tell him his appeal was unsuccessful (of course).
At some point in this period between firing and the appeal, the employee will have to go off to ACAS for ‘pre-action conciliation’ where somebody will phone the employee and the employer and ask whether they can’t come to some sort of deal.
The employee is still fired.
If no deal is done during the period ACAS is involved, ACAS issues a certificate confirming that they were consulted and armed with that the employee finally gets to
Well, tribunal actually but pretty much the same thing these days.
They have to do that within 3 months of the date they were fired (with the time limit expanded in excitingly non-obvious ways by the period ACAS was involved). If they don’t, tough.
They are still fired.
The employee has to show that the dismissal was unfair. In practice that does tend to mean that the employer has to justify it by reference to one or more of the allowed reasons.
Since one of the reasons is ‘any other substantial reason’ they don’t really have to try too hard. In this example you’d be looking pretty squarely at ‘conduct’ being the reason.
The employer does not have to show that the employee did enrich the menu with their ‘special sauce’.
They just have to show that they reasonably believed he did and that a reasonable employer could decide to dismiss based on the facts as the employer believed them to be.
The tribunal might well consider that it was all rubbish and that the employee didn’t do it but that’s irrelevant.
Even if the tribunal holds that the dismissal was unfair, the employee is still fired in most cases.
It is possible for a tribunal to order reinstatement but that is incredibly rare and will usually only be ordered where both sides state that they are happy for that to happen. So in practice, almost never.
