The French shell out to have an engine turned over inside in a surgical procedure (10)

'a surgical procedure' is the definition.
(laparotomy is a kind of surgical procedure)

'the french shell out to have an engine turned over' is the wordplay.
'the french' becomes 'la' (one of the French words for 'the').
'shell out' becomes 'pay' (I've seen this in another clue).
'to have' indicates putting letters inside.
'an engine' becomes 'motor' (I've seen this in another clue).
'turned over' shows that the letters should be reversed in order.
'motor' backwards is 'rotom'.
'pay' enclosing 'rotom' is 'parotomy'.
'la'+'parotomy'='LAPAROTOMY'

'inside in' is the link.
I am not very happy about this link. Some or all of it may belong to another bit of the clue.

Can you help me to learn more?