A preliminary question. It sounds like this was prior to the Succession Regulation coming into force in 2014. However as the testator has not yet deceased, you will need to check through the ramifications of its coming into force on the current will .
Were they appointed as Executors under an English law Will or as "executeurs testamentaires" under a French law will?
Or was it a French law will dealing with English assets and appointing an English Executor?
Whilst not decrying our French colleagues, unless the notary was actually qualified as an English solicitor, I would be curious to know what was actually drafted for the French resident testator.
If the latter the individuals designated as executeurs testamentaires can refuse to accept the mandate implicit in the rôle of an executeur testamentaire and therefore not act under French law. The heirs or legatees would then be left to deal with the French succession in France and elsewhere.
Can't be of assistance without more details on the actual document and the law purporting to govern it - let alone the habitual residence point or nationality option under Regulation 650/2012.