Please look at their web-site here.
Here are some rather odd things about it, to pique your interest (my emphasis) . . .
It is registered with the Charity Commission for England and Wales as nbr 1042395 - FRANCO-BRITISH COUNCIL - BRITISH SECTION.
Notes from its Defence Conference in Nov 2016 (confusingly accessed by a link on their main page entitled "For the 2017 Defence Report", and also entitled "2017" at the top of page one but referenced by every subsequent page footer as "2016") concluded on page 4 that the Brexit vote should have no impact on the direction of travel ("Tout va bien"). Mysteriously no reports from subsequent meetings seem to be available, although at least one such is believed to have taken place in March 2018.
It is legitimate to ask why a charity is getting involved with Defence, which is above all a matter for the national governments. Are charities not required to be apolitical?
According to the Charity Commission, for charitable purposes a political purpose includes "securing or opposing a change in the policy or decisions of central government or local authorities or other public bodies, whether in the UK or overseas". It is hard to see how bilateral cooperation in matters of Defence can be regarded as apolitical, but maybe they are simply not seeking to change the established policy since 1972.
Also according to the Charity Commission, "to be a charity, an organisation must be independent of outside control in a way that would prevent it being subject to the control of the High Court" (I don't understand that either - if anyone can enlighten me please use our Contact page).
At this point we really want to know where the FBC gets its funding from. The FBC web-site lists funding sources (as at 21st January 2018):
So there we have it - our Defence policy is being influenced by a charity set up when the UK joined the "Common Market", funded by British and French government agencies and a collection of businesses / businessmen with very large international interests.
The "Leaders" programmes are vaguely defined but could be designed to select and indoctrinate malleable young people to promote unspecified values across the businesses and institutions of the future.
One might think that such an opaque programme should automatically disqualify the FBC from charitable status?
Nowhere does this influence include any democratic input and to retain its charitable status it is honour-bound not to attempt to secure a change in the current policies of government.
The further integration of British armed forces into the EU of M. Macron is progressing unimpeded by any Brexit referendum decision and apparently out of reach of any democratic oversight.