Officer flanked by two middlemen in Parisian establishment, maybe? (5)

'establishment maybe?' is the definition.
I know nothing about this answer so I cannot tell whether this works.

'officer flanked by two middlemen in parisian' is the wordplay.
'officer' becomes 'col' (short for colonel).
'flanked by' is an insertion indicator (other letters go on other side).
'two' indicates the doubling of some letters.
'middlemen in parisian' becomes 'e' (I can't explain this - if you can you should give a lot more credence to this answer).
'e' doubled is 'ee'.
'col' inserted into 'ee' is 'ECOLE'.

Can you help me to learn more?