For the passengers on flight AF1068, departing from Charles de Gaulle Airport at 12.55pm, it was probably one of those occasions when Roy Keane might as well have hung a sign around his neck saying: Do Not Disturb.

There was once a time when he and Sir Alex Ferguson might have imagined this kind of chance meeting would be a pleasant occasion. They could have caught up, shared a few stories and been reminded how, in happier times, they were drawn together by their competitive courage in the name of Manchester United.

Instead, it is fair to say there was a distinct lack of entente cordiale as the two men crossed paths for the first time since using their latest autobiographies as a form of artillery to shoot one another On one side, down. Keane sat impassively by the window. On the other side, Ferguson was three rows back. Two men who once had so much in common but who now give the impression they would rather not share one another’s oxygen. The plane had not even taken off before another passenger was speculating whether the flight might have to be diverted due to air-rage.

The first thing to report is that Keane decided not to prove Ferguson’s theory that “the hardest part of Roy’s body is tongue”. The two most impenetrable stares since General Zod did not lock and the former United captain evidently did not feel this was the right place to challenge the older man about the “lies, basic lies” within Ferguson’s book.

Ferguson, in turn, did not rev up the infamous hairdryer and opted instead for his other well-rehearsed ploy of trying to freeze an old adversary into indifference; both he and Keane studiously ignored one another as they passed in the terminal. Ferguson and his wife, Cathy, had been first on the flight after he was recognised by a member of Air France’s staff and moved to the front of the queue. Keane was the last after hanging back. As the Irishman took his seat, Cathy gave her husband a nudge. Ferguson took one look, narrowed his eyes and then lifted up his newspaper to continue reading the sports pages. That newspaper was a handy shield over the next hour or so in the air.

What is difficult to know is how the two men reacted when they saw one another among the pastries and fruit juices of Air France’s VIP lounge and realised they were about to share the business-class seats back to Manchester. Perhaps that was the moment Keane challenged Ferguson about using his “friends in the media” to put out various lies about him. Or maybe this was the chance for Ferguson, in Paris because of his work with Uefa, to tell him to keep his nose out of the Rock of Gibraltar business. We will probably have to wait until the next book. Though it is fair to say that if things had got out of hand there were plenty of people to get in between them; a squad of French rugby players were on the same flight.

Spare a thought, though, for Paul Scholes bearing in mind he was travelling with Keane, having been another part of ITV’s coverage of Chelsea’s 1-1 draw against Paris St Germain. Scholes’s presence as the man in the middle merely added to the sense of awkwardness. Cathy seemed pleased to see him, but maybe this wasn’t the time to beckon him over for a chat.

It ended without so much as a backward glance. Keane was off the plane first while Ferguson hung back this time and, more than anything, it felt slightly strange to see the former manager and the former captain, two of the people who have been most prominently involved in the United success story, reduced to giving each other the silent treatment. No doubt they will both blame one another.

Their feud has been a captivating story and offers a fascinating insight into their personalities and flaws. But they really do need their heads knocking together.