The movement in the lycees, attended by students aged 15 to 18 for their final three years of secondary education in France, has angered the government.
Since last week, students have staged protests outside schools over grievances ranging from timetables, class sizes and a shortage of teachers to overheated classrooms during this year's heatwaves.
The protests started in the Ile-de-France region around Paris but have now spread to other cities nationwide.
On Wednesday, 625 people were detained during high school blockades, Interior Minister Laurent Nunez said, noting an "expansion of the movement" and condemning an "escalation of violence" outside certain schools.
Eighty-three police officers and gendarmes were wounded on Wednesday during the protests, which affected a total of 356 schools, he added.
The minister slammed the "targeting of law enforcement officers, the throwing of projectiles, acts of violence, verbal abuse, attempted arson, and what amounts... to urban violence."
Since the start of the unrest last week, 119 students and staff members have been injured, Education Minister Edouard Geffray said.
The cites worst affected Wednesday included Paris, Bordeaux in the southwest and Lyon in the southeast, and the northern city of Lille where police again used tear gas in clashes, AFP correspondents said.
"It is imperative that our students be able to return to class —especially those who are currently prevented from doing so," Geffray said.
Speaking in Madrid, President Emmanuel Macron slammed hard-left politicians he accused of "legitimizing violence" in the French school protests.
"We don't condone vandalism; we came to defend our rights because we have horrendous schedules -- we work 8:00 am to 6:00 pm and that's not right," Juan, from the Montbello high school in the northern city of Lille which had been blockaded over the last days, told AFP.