An internal report prepared for the Paris police department which was leaked to the media analysed the opening of the movement in Seine-Saint-Denis. It concluded that students were being “egged on by far-left elements from students unions… and political groups such as… LFI.”

It said the tensions “could be part of a flame-kindling strategy… aimed at imposing their ideas ahead of the national elections”.

In support of its conclusion, the report’s writers cited the presence of protesters who are not themselves lycéens, the vagueness of the demands, the flying of Palestinian and Algerian flags, and the use of tactics – like calling for supplementary protests at police-stations – that come from the radical-left playbook.

The LFI strongly denies doing anything more than lending its natural support to a movement it regards as legitimate. On Thursday Mélenchon called on students to avoid violence “which only serves our enemies’ interests”.

But his opponents believe that the 75-year-old veteran – who stands a good chance of making it to the second round of the presidential elections in May, probably against the hard-right’s Marine Le Pen – knows exactly what he is doing.

Polls show he has massive support – some 40% — among 18-24 year-olds in France, and that this is concentrated in the populous, high-immigration city suburbs where his talk of a “new France” and “creolisation”, to reflect France’s changing language and population, are highly appreciated.

But young people are also the biggest abstainers in French elections, so the strategy – as the elections approach – will be to give constant reminders to this part of the population that the LFI is at their side, and that their vote can count.

Whether this will be enough to ensure victory for Mélenchon is another matter. He must surely take seriously the polls which all show him losing massively in a run-off against Le Pen.

If that happens, France will be in very unstable territory – for which the young people’s protests of recent days will indeed have been a harbinger.