Hi Maddy,
As the received signal strength degrades, all that happens with an analog radio is that the background noise keeps increasing until eventually you can no longer distinguish the broadcast programme.
On the other hand, digital radios require a strong signal strength so that they can convert (with no errors) the digital broadcast into analog.
The digital service is either on or off, so once the signal drops below the digital threshold, no reception is possible - and this will happen much sooner than analog.
Solution:
BBC World Service can be heard the whole world over, but on Short Wave - so if are using a car type radio with FM and AM, then the signal will disappear in upper / middle France.
A good quality short wave radio like the higher priced models from Sony or Roberts (actually Sangean) should have no trouble - especially if you get a list of the transmission frequencies from the BBC web-site
Robert