I think that if they remain in France, then under current rules, 'their' children may not be entitled to a UK passport, these rules have changed since I had my children, that I do know.
And health care, well, as was shown, EHIC's are essential at the moment. Even for us when we lived in France, we would take our CEAM's back to the UK with us in the hope that we didn't need them.
After Brexit, if it happens, no one really knows what will happen with health care when visiting the UK as non resident. Something to look into at a later date.