A friend of mine is planning to come to London in April but she knows that her French ID expires while she is here. As far as the French authorities is concerned an expired ID card is still valid for the next 5 years. Will she have problem at Immigration at Gatwick airport when she goes back to France?
As you noted, a French ID card delivered between 2004 and 2015 has its validity extended by 5 years.
Les autorités des pays suivants n’ont pas officiellement transmis leur position quant à leur acceptation de la carte nationale d’identité en apparence périmée mais dont la validité est prolongée de 5 ans comme document de voyage :
-(...) Royaume-Uni (...)
Returning to your country of (legal) residence is a special case of travel, in that your home country is obliged to accept your return. You may of course have issues proving what your home country is, but here that doesn't seem to be an issue as France recognized your ID.
That said, special cases are far more likely to draw attention, and it can take a while to figure out the legal situation here. The airline is in no way obliged for that, so there's nobody to blame when you miss your flight due to this.