Mr Allan, OOCL's transatlantic trades director 10 years ago, died a day after falling down a lift shaft on the newly-built 4,402-TEU OOCL Montreal during a customer reception on board the ship in Le Havre.
The Tribunal de Grande Instance in Le Havre will deal with whether and to what degree the death was caused by clumsiness, carelessness, inattention, negligence or breach of duty to care and safety.
A French prosecutor has made a lengthy inquiry into the failure of lift system, which has never been explained, said Lloyd's List. Mr Allan, 53, had called the lift to the bridge, stepped in not realising it had not arrived.
Said an OOCL spokesman: "We cannot comment on the case as the proceedings are in progress."
Over the years a number of investigations and reports have been carried out into the incident, but without any satisfactory outcome for the family.
An elevator expert, hired by the victim's family, said: "It is considered likely that the incident occurred as a result of either the door-lock safety circuit being shorted out and thus deceiving the controller into thinking that the doors were working properly.
"I am firmly of the view that this incident is likely to have been caused by human intervention and have seen no evidence to suggest that the lift system was faulty, but clearly the door-lock receptor has been subjected to an unauthorised out-of-design modification," the expert said.
Said Hayden Allan, the victim's younger son: "We are pleased that this day has finally arrived. Our father would have expected nothing less than for us to campaign for justice and to prove the facts in this case."