In the case of FR they bought Buzz and gained their UK AOC that way and may operate from UK to non eu countries.
In EI's case they've piggie backed on Astraeus' AOC and can now do the same as Astraeus also have 1 x A320. EI crew in LGW and BFS are now being trained with the Astraeus AOC and can operate UK to non eu destinations such as Moscow, Agadir, Tunis, Cairo etc but only with A320's NOT A330's. Whether FR's or EI's reg's have EI or G on the tail doesn't matter. Hence Monarch have EI reg aircraft.
Hope I've made that clear as possible.
PS '5th freedom' only occurs when you originate the flight from another country. Besides you're limited in the number of passengers you can pick up in the transit airport.