French high-school students face an anxious wait for exam results this week amid protests by teachers who are threatening not to hand over results and an embarrassing leak of baccalaureate maths papers.

Police arrested 19 high-school children on Tuesday and Wednesday in Marseille and Paris as part of an investigation into the leak of a maths paper sat by thousands of students which was shared via text message and WhatsApp in June.

Seven have been released, while 12 remain in custody and could face charges of exam fraud, breaching trust and conspiracy, the Paris prosecutor’s office said on Wednesday.

French education authorities have decided for the time being not to cancel the exam, which was sat by about half of the 740,000 students who completed their baccalaureate this year.

The education minister, Jean-Michel Blanquer, faces another crisis caused by markers in some regions, who are threatening not to return exam papers as part of efforts to resist changes to the end-of-school exam from 2021.

Results are due to be published on Friday.

“At this time, I must admit there is a small risk, but we’re doing everything we can to make sure it doesn’t happen,” Blanquer told the French TV station BFM.

“I have told the teachers who have decided to play this game, which completely goes against the principles of public service, that there will be very severe financial consequences,” he added. He threatened to cut “up to two weeks” of their salary.

The strike affects 108,000 of the 4m exam papers submitted for marking, the “Block Blanquer” group of protesting teachers has said.

The teachers are trying to convince the government to reopen talks on an overhaul of the French baccalaureate from 2021, which will mean more continuous assessment and less dependence on final exams.

Thousands have taken to the streets around France in recent months. Some have occupied classrooms overnight while others have dressed in black during protests to “mourn” the exam.

The French president, Emmanuel Macron, pledged in his 2017 election campaign to overhaul the bac, saying it was failing to prepare teenagers for university and the modern job market.

Blanquer has argued that the education system relies too heavily on final exams.

The famously tricky baccalaureate, based on a structure created under Napoleon in 1808, includes philosophy brain-twisters such as “Do we always know what we desire?”

It is not the first time France has grappled with leaked exam papers. Four students were handed suspended sentences last year after a maths problem leaked on an internet forum in 2011.