Tricky one. Empress Eugénie founded the abbey of St.Michael in Farnborough specifically as a last resting place for her husband, her son and herself. It's really got nothing to do with the British government as they have no jurisdiction over the abbey.
If the French government wishes to repatriate the remains of their last emperor, they will have to negotiate with the Abbot of St.Michaels and with the legal executors of Empress Eugénie's will (whoever they may be). The British government can only advise in this matter.
Tomb of Napoleon III in the crypt of St.Michael's Abbey, Farnborough (three representatives of the Souvenir Napoleonien came from France to hear Mass and pay their respects at the tomb of the Emperor on the anniversary of his death, 9th January).: