Protests over France's failing school system will only 'intensify' if demonstrators' demands are not met, the country's main high school union has warned. 

Hundreds of thousands of protestors have caused havoc in France's major cities this week over dilapidated classrooms, overloaded timetables and school buildings incapable of coping with rising temperatures. 

Demonstrators let off flares, set buildings alight and hurled rocks at police officers as more than 256,000 took to the streets on Tuesday. 

Riot police covered in body armour used shields, batons, pepper spray and tear gas to push back demonstrators in the capital, while in southern cities such as Marseille and Bordeaux officers were pictured spraying crowds with water cannons. 

More than 500 schools were forced into either partial or complete closure as riots intensified on Monday. In some cases, schools were even 'burned or ransacked' by raucous crowds. 

Figures produced by the country's Interior Ministry revealed a staggering 6,100 rioters have been arrested since the outbreak of protests in September. 

Yet the co-secretary general of France's main high school union, Syndicale Lyceenne, has now insisted that protests will only escalate as long as students 'are not listened to'. 

Marius Mesnil told local broadcaster BFMTV: 'It shouldn't be up to us high school students to block high schools, to go and demonstrate by the hundreds of thousands in the streets to study in normal premises. 

'The government has been trying to make us believe in recent days... that the movement has lost steam. Today we see the opposite.' 

Unions are calling for an end to the country's substandard school conditions, with thousands complaining of missing teachers and overloaded timetables.

Students insisted once more last night that they are 'really, really motivated' to continue their fight until they're given a 'real answer' by the authorities. 

One protestor, Lina Mas, said: 'It gives us a lot of hope because we are always blamed for being on our phone, but we are more educated than they think we are. 

'We're going to block everything until we have what we want.' 

Another, named Alissa, said: 'We're going to the streets because they've closed our schools... schools are falling apart.' 

While a protestor in Paris called Carole, aged 17, complained: 'Classrooms are full of rats and teachers are not always present - the conditions are terrible. 

'Students from ethnic minorities are also terribly treated – especially by the police. This is why we are out on the street.’

Yet across the country many demonstrations quickly turned violent as schools were blocked off and protestors, many of whom donned balaclavas, clashed with police.  

Shocking images from Paris showed rioters setting alight bins, letting off flares and clambering over statues yesterday in chaotic scenes.

At the Place de la Nation, one of the city's most iconic squares, local police officers told reporters they are being repeatedly targeted by hordes of youths. Many protestors were heard shouting: 'Everyone hates the police!'.

One officer said: 'Gangs of youths are trying to attack us constantly.'

Such scenes were however far from confined to the streets of the French capital.

In Rennes, police were pictured using water cannons and batons in a bid to ease the chaos ensuing around them.

Meanwhile, French newspaper Le Parisien reported that some inciters were telling their Snapchat followers to 'bring knives' and 'stab civilians in the crowd' outside the Couffignal high school in Strasbourg.

Similar scenes were also replicated in southern French cities such as Marseille, Lyon and Bordeaux.

It came less than 24 hours after a 15-year-old schoolboy lost his left hand when a police grenade exploded in Lens, around 150 miles from Paris.

Footage from the scene showed several people tending to the young man as he lay on the pavement. His left hand appeared to be missing, with a bloody stump in its place.

He was later seen slowly walking away from the scene. Other reports claim he lost his arm up to his elbow but this has not been confirmed. 

A spokesman for the ministry, which earlier estimated that more than 250,000 people protested on Tuesday alone, said: 'There have been 6,100 arrests, 1,483 of them minors, since the protests began three weeks ago.'

All were taken into custody for a variety of public order offences, from violence against public officials to vandalism.

At least 715 officers and 215 teenagers have been badly injured in clashes, the spokesman added. 

Figures from the political Left have been accused of encouraging riots in a bid to boost their vote, with a number of politicians joining protestors on the streets this week.

One of those yesterday was Jean-Luc Melenchon, the France Unbowed hard-Left presidential candidate, who previously accused the country's current government of 'steadily dismantling public services'.

Mr Melenchon has a serious chance of replacing Emmanuel Macron as head of state in 2027 when Mr Macron will be forced to stand down having spent two terms in office.

A Toluna Harris poll last week suggested that Mr Melenchon and Marine Le Pen, of the far-Right National Rally, would advance to next year’s presidential run-off, with Le Pen best placed to win.

Bally Bagayoko, the Left-wing mayor of the Parisian suburb of Saint-Denis, was another of those to join rioters in the capital.

He said he opposed violence but adamantly stood by the thousands of protestors causing chaos on the streets of France.

'I stand by being on the side of my residents, and high school students are my residents,' he said.

The French Greens, meanwhile, called on elected officials and parents of rioters to join in wearing 'with white helmets, white armbands, white clothing, to go and protect our children in the demonstrations'.

Green leader Marine Tondelier spoke in front of a high school in Lens – the city where the teenager's hand was blown off by a stun grenade on Monday – saying: 'All political families together should have this concern to allow our young people, those who wish to do so, to express their demands in safety.'

Prime Minister Sebastien Lecornu's office called for 'peaceful' gatherings and a return to 'a structured, legal and democratic form of opposition'.

He also ordered government officials to tackle the students' main demands, including ensuring absent teachers are replaced, reviewing the length of the 8am to 6pm school day and the need for longer lunch breaks.

The government would also look at repairs needed to ageing school buildings, said Mr Lecornu, who demanded ministers send in their first proposals by the end of October - but finding spare cash will be difficult.

The protests have piled pressure on a government trying to narrow a ballooning budget deficit as investor concerns about France's growing debt pile, weak growth and reluctance to rein in spending push bond yields higher.

The yield on France's ten-year bonds briefly hit a 24-year high of over 5 per cent last week.

The surge in French borrowing costs has started to spill into the broader euro area, with the sliding euro currency the latest alarm bell for policy makers.

Finance Minister Roland Lescure said on Tuesday there was no need for the European Central Bank to step in.

The head of the CGT labour union Sophie Binet has said its members would be there to 'protect high-school students'.

Several unions have accused the police of using disproportionate force against the protesters.

The police have launched ten internal investigations into allegations of brutality since they started, Interior Minister Laurent Nunez said late on Monday. He added that the police response has been proportionate in 'almost all cases'.

'The only response they've received so far is repression,' Sigrid Gerardin, a Paris high school teacher, said of the pupils.

Felix Barney, a university student, described the police response as disproportionate. 'It doesn't have any sense to hit minors,' he said.

The government has sought to address the grievances, while accusing hard-Left activists of having hijacked the protest movement.

It is also pushing legislation to make those responsible for damaging public property pay for repairs themselves, instead of using public funds.

Mr Lecornu said the draft law could allow compensation payments to be recovered from family allowances and housing benefits while ensuring a minimum income.

Union leader Ms Binet meanwhile said it would 'end up targeting the most vulnerable families'.

The hard-Right National Rally (RN) party had an even firmer proposal. RN representative Sébastien Chenu, who is also the vice-president of the National Assembly, called for families of rioters to be punished if their children take part in these protests.

He said: 'We must act using this lever of cutting benefits, we must go further and evict people from social housing if their child misbehaves.'