Wednesday is the 25th anniversary of the road accident which killed Princess Diana and Dodi Al-Fayed in Paris. Next Monday is the 10th anniversary of the Al-Hilli murders in the French Alps.

What do these two events have in common, other than the proximity of their dates?

They are both – still – the object of wild conspiracy theories.

In both cases, if you look at the undisputed facts, the possibilities are limited. The Diana accident could only have been an accident. The Al-Hilli murders were almost certainly a random act by someone local.

Neither of these explanations is satisfactory to a chunk of the popular media – in France as well as in Britain. Wild notions still thrive.

I reported both events at the time. I have studied them in some detail. The sequence of events makes any form of assassination impossible (in the case of Diana and Dodi’s death) or extremely unlikely (in the case of the Al-Hilli murders).

In both cases, the French investigators have been criticised in the UK media. Is there any truth to the criticisms? A little; not much.

What is certainly true is that both events illustrated the huge gulf between the ways that French and Anglo-Saxon investigators deal with the media.

In theory, every party of a French criminal investigation is secret once it is handed over to an examining magistrate or juge d’instruction. In the case of the Diana accident in 1997,  the investigating magistrate, Hervé Stéphan, took that principle seriously. In the first couple of weeks, very little information, beyond the basic facts, was given to the world media assembled in Paris.

Together with a BBC colleague, Hugh Schofield, I  wrote to Judge Stéphan at the time. We said we understood the French system but unless he allowed the official findings to be released, a thousand conspiracy theories would breed.

He wrote back to say, in effect: “You are absolutely right but my hands are tied. Rules are rules.”

By the time of the Al-Hilli murders 15 years later, it seemed to me that that the French judicial authorities had learned their lessons from the information débacle in the Diana case. The Annecy chief prosecutor, Eric Maillaud, gave regular press conferences. Some of the leading gendarmerie investigators took part.

Even so, the information was limited and strangely filtered. It took a big leak to Le Monde in November (two months after the event) to establish the basic time-line of what happened in a forest lay-by near the village of Chevaline on September 5th, 2012.

Once again, the absence of fundamental information allowed wild theories to take hold.

Take the accident in Paris first. There are some areas of uncertainty. A white Fiat which struck Diana and Dodi’s limousine has never been traced. But the undisputed facts make it impossible for anyone to have organised an assassination attempt and disguised it as an accident.

The route taken by Diana and Dodi that night was random. They were trying to shake off the paparazzi on motorbikes who were pursuing them from the Ritz Hotel. Rather than go straight back to Dodi’s flat just off the Champs Elysées, they took a large detour along the fast quais beside the river Seine.

Their driver was the worse for both drink and drugs. He was actually heading away from Dodi’s flat when he crashed into a pillar in the tunnel below the Place de L’Alma.

How could anyone – M16, CIA or the Royal Family – have known that their limo would have been in that place at that time?

Now, the Al-Hilli murders.

All sorts of intriguing or suspicious-sounding information has been unearthed by the media about the three victims: Saad Al-Hilli, 50, his wife Iqbal, 47, and her mother Suhaila Al-Alaf, 74. Similar theories have been advanced to suggest that the real target of the murders was Sylvain Mollier, 46, the local cyclist found dead beside the British-Iraqi family’s car.

Both the Al-Hillis and Mollier took random decisions that day to drive or cycle to the end of a winding, bumpy 3 kilometre road into the forests and mountains above Lake Annecy.

Witnesses saw no sign that they were followed. It is difficult to imagine how a murderer – contract killer in the case of the Al-Hillis; someone with a personal grudge in the case of Mollier – could have been lying in wait for them at that isolated place at 3.30pm that afternoon.

The forensic evidence found at the scene suggests that killer was there when they arrived. It also identifies the gun used as a 70 years old (at least) 7.65 mm P06 Luger, issued to the Swiss army and police until the end of the 1930s. That is scarcely the weapon of choice for a contract killer.

After dutifully following all possible leads about Saad Al-Hilli’s business activities as a microsatellite  engineer and his quarrel with his brother about their father’s will, French investigators long ago reached a working conclusion. The murders were a random act by a deranged local man, who has since died or is still lying low.

Conclusion: the French policy of “secrecy of the investigation” encourages wild interpretations, and pure invention, to prosper. Twenty five and ten years later, the collective, popular memory – especially of the Princess Diana road accident – retains the wild theories. It is often hazy on the facts.