THREE French institutions—trains, strikes and philosophy—collided this morning to create a near-perfect political storm. On June 16th a rolling national strike by trade unionists at the SNCF, the national railways, entered its sixth day, disrupting the start of the countrywide philosophy paper at the annual baccalauréat exams. It is the worst industrial action that François Hollande has faced since his election to the presidency in 2012.

The two unions leading the strike, the Communist-linked CGT and the even tougher-talking SUD, are against the government’s plans to merge two companies: the heavily indebted RFF, which runs the tracks, and the SNCF, which manages the trains. Although no jobs are at stake, the unions suspect that this reform could lead to changes in work practices, and want the government to take on the debt. In a meeting with SNCF management on June 16th, they also pressed for pay rises.

When the strike began on March 11th, it looked as if it might be short-lived. Yet it has already gone on longer, and been more far-reaching, than expected. In some regions, half of all TGV fast trains have been cancelled for the past six days, as well as half of regional trains and two-thirds of suburban trains into Paris. The SNCF says that this has already been the most costly strike for 13 years. The unions plan a seventh consecutive strike day on June 17th.

For the two unions leading the strike, the industrial is in part a reflection of their weakness, not their strength. Unions as a whole are divided: the more moderate CFDT, for example, is against the current strike, and backs the planned SNCF reform. Both the CGT and SUD are under particular pressure from their grass-roots to flex their muscles because industrial action has lost much of its punch. The sort of paralysing strikes once wearily common in France have become rare. By law, public services have to run a minimum service during strikes, and days of industrial action are no longer paid. Between 2005 and 2011, the number of days lost to strikes per 1,000 employees fell from 164 to 77.

Yet the timing of this strike, reaching into the baccalauréat week, is also a public-relations risk. Every June, as part of a national ritual, over half a million school-leavers sit down to take the first bac exams. For half of them, this involves a four-hour philosophy exam based around a single essay question; this morning’s choices included “Do we live in order to be happy?” The prospect of pupils arriving late due to the train strike has prompted much indignation and an emergency scheme by the SNCF to encourage car-pooling and other alternatives.

For its part, the government seems to be betting that public incomprehension, combined with divided unions, will undermine the strikers’ ability to hold out. Manuel Valls, the prime minister, said in a radio interview that there was “no question” of shelving the reform. There have been months of discussions with the unions already, he added. It will be debated in parliament on June 17th.

At a time of high unemployment and economic stagnation, there is little sympathy for those in protected public-sector jobs, least of all railwaymen. The French are well aware that train drivers still get extraordinary perks, including retirement for most train drivers at the age of 50. Laurent Berger, the moderate CFDT leader, has accused the striking unions of “contempt” for bac pupils. As it is, participation in the strike has dropped from 27% of SNCF workers on day one to 14% on June 16th.

Yet this is all the same a perilous moment for the Socialist government. It is the first real test of its ability to face down industrial action, and comes at a time when Mr Hollande’s popularity is dismally low and distrust of the moderate Mr Valls within his own Socialist Party is high. The prime minister is also trying to push controversial public-spending savings through parliament, as well as cuts in social charges for companies, both of which are regarded by the left of his party as a betrayal of campaign promises.

Mr Valls can ill afford to let the chaos on the railways continue. But, billed as a bold reformist who would be tough in a way that Mr Hollande has failed to be, he cannot be seen to give in at his first test on the streets either.