There were already demonstrations outside 261 schools on Monday, which the education ministry said had been blockaded.
In the western suburb of Nanterre in Paris, dozens of students clashed with riot police who fired rubber bullets.
Shop windows were reported broken in the Saint-Denis suburb, where education officials said more than half the areas secondary schools had been blockaded.
In Lyon, several cars were burned and one teacher whose car was badly damaged by fire complained: "They want to fight [against the pension reform]. OK, but they have to understand the meaning of what they are doing".
In other developments:
* Outside the Grandpuits refinery, east of Paris, strikers burned tyres in defiance of a government order that the facility should be reopened.
* In some cities, such as Toulouse (south-west) or Saint-Etienne (centre), public transport depots were blocked on Monday morning, preventing buses and tramways from operating for several hours.
* Rail traffic was being disrupted with one in two fast TGV trains running, and one in three normal-speed trains running.
* Although the Eurostar train service between Paris and London is normal, there is no Eurostar service between Brussels and London on Monday due to a strike in Belgium.
* A key fuel pipeline that supplies the two airports in Paris has been restored, but the civil aviation authority is warning airlines operating at Charles de Gaulle to arrive with enough fuel to make the return journeys.
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