and this is exactly the issue.
Yes, at FL090 heading towards say Lydd will place you firmly into UK Class A, but unless you get a handover to London Control you are not going to get a service in that airspace.
Even though you are
in CAS continuously.
LFAT will probably clear you initially to FL080/090 or so and that is now your vertical clearance. Your filed route remains your lateral clearance.
If at that point you lost comms, then as per international IFR rules, you would fly the filed route, climbing to the filed level at some appropriate point. You had an IFR clearance out of LFAT and you stay with that, because you never cancelled IFR.
But you won't lose comms
You will be handed by LFAT to "London 124.6" which is London Info, and they will tell you to descend below CAS. That is what is wrong here. It is a lack of coordination capability between the "smaller" French units and London Control. I don't know any more about the background. I have asked various ATCOs but nobody seems to know.