the exchange is noted as being translated from the original French, which accounts for its unnatural feel perhaps?
Here in France, any reporting on the transcript is clear that it comes from UK sources. I think that means that Willie McKay released it to the UK press having gained it from his son Jack who plays for Cardiff and having spent a considerable time in France, probably speaks French. I also think the transcript has been tidied-up to make it understandable because any text exchanges I happen to see between my kid's and friends are full of French colloquialisms!
The media here are also stressing the point that McKay has clearly stated that neither he nor his sons (two players and an agent) have any connection to the aircraft in question. They also state that they have contacted one person in the past, who runs an aircraft consultancy, to arrange flights around Europe which is exactly what they did this time.
Finally, while this incident is not getting the same level of coverage in French light aviation forums as it is in the UK, I have noted a couple of comments raising the question of how a passport from someone not actually in France was scanned or photocopied in Nantes