I take it you are hoping to receive BBC on FM, DAB or possibly BBC world service on shortwave. (you don't give any clue), somewhere between La Rochelle and Bordeaux, using an outside TV aerial. In short, it ain't gonna happen for FM or DAB. BBC World service is available in some places in France on local FM radio - See http://www.bbc.co.uk/worldservice/europe/radio/france_1.shtml
These pages will give you more info, but it ain't looking good:
http://www.bbc.co.uk/worldservice/schedules/010116_weurope.shtml
http://www.french-waterways.com/france/radio-tv.html
A satellite box for radio and TV doesn't need to be expensive. The only caveat really is to make sure the dish is large enough because France won't be in the main part o fthe footprint.
http://www.ebay.co.uk/itm/like/160575756517?adgroupid=&hlpht=true&hlpv=2&rlsatarget=&adtype=pla&ff3=1&lpid=122&poi=&ul_noapp=true&limghlpsr=true&ff19=0&device=c&chn=ps&campaignid=&crdt=0&ff12=67&ff11=ICEP3.0.0-L&ff14=122&viphx=1&ops=true&ff13=80
So some research on dedicated expat and enthusiast forums.
And it's coaxial, not coaxle; omnidirectional, not omnidirection and expense, not expence. ;-)
XXXXX, September 2015