Sorry to disagree.
First "flames out the back of an engine" is
unlikely to be an Engine "Fire". Anyone who knows the first principle of a Jet Engine will know this characteristic of a "surge" "stall" and typical of the damage cause by a birdstrike. The "damage" "stall" may require shutting down the engine to clear it, the engine may be available for relight, either in emergency, or just if desired (particularly if the EGT did not exceed the limit).
Very unlikely to result in a "fire" warning...
Again, if you had clue what you are talking about, it is often SOP on a 4 engine aircraft to continue to destination on 3 engines. For instance I know BA recently did this with a major surge ex LAX shortly after TO - got back to LHR. Assuming the engine is secured satisfactorily, where to land will often be dependant on where maintenance is etc. and often "get home as far as possible" is used.
All this was obviously poorly handled
Glad you are able to slag people off like this...
The Diversion yes/no to NCE would be for fuel. Again, if you knew what you were talking about, after an engine failure, the fuel consumption increases. Sounds a close run thing as to whether CDG could be reached, but weather, refining fuel calcs, SOPs, seems it could.
Seems handled fine to me, except maybe comms with the passengers. Given my p*ss poor French, not sure I could have got the message across either
