Take the silly case of Lydd to Le Touquet. You cross the FIR boundary, switching from the Lydd Frequency direct to the LTQ frequency.
According to my interpretation of the rules, you should contact Paris North FIS first, and if contact is not possible with Paris North, you should contact Calais, before switching to LTQ. I know it sounds silly and doesn't happen in practice, but ...
The unit to be contacted
The radio contact must be established first with the flight information
centre (FIC) or flight information sector (FIS) concerned.
If it is impossible to establish radio contact with the FIC or the FIS
concerned when crossing the border, the pilot must contact preferably
the air traffic control units set up on the aerodromes, which are listed
below, in order to transmit them the «border crossed» message.
Border aerodromes concerned:
Border crossed report:
The mandatory report message shall include information:
- aircraft registration;
- aerodrome of departure/of destination;
- “border crossed” indication;
- position/altitude/time;
If it was not possible to transmit the “border crossed” message when
crossing the border, the message must be completed by the position
and altitude when the transmission is possible.
Contact not possible
If the pilot cannot make this contact for reasons against his will, he must,
after landing, contact the police and customs services and the local air
traffic control units concerned or, otherwise, the Area Control Center
(ACC) concerned:
AJACCIO NAPOLEON BONAPARTE LFKJ
BALE MULHOUSE LFSB
BASTIA PORETTA LFKB
BIARRITZ-BAYONNE ANGLET LFBZ
CALAIS DUNKERQUE LFAC
CHAMBERY AIX-LES-BAINS LFLB
LILLE LESQUIN LFQQ
NICE COTE D’AZUR LFMN
PERPIGNAN RIVESALTES LFMP
STRASBOURG ENTZHEIM LFST