The future of the European exchange rate mechanism and planned currency union probably depends on which way the French fall.
The President's problem is how to maintain a strong franc, low inflation and an improving budget deficit while reducing an unemployment rate that ranks among the highest in Europe. These policies are normally regarded as contradictory. Chirac has set himself the apparently impossible task of proving they can be complementary.
The first stage came on Tuesday when Alain Juppe, the prime minister, unveiled plans to attack unemployment. This was a key election promise, since the overall rate currently stands at 12.2 per cent of the workforce, or 3.3m, while youth unemployment is a disturbing 25 per cent.
The prime minister's measures include waiving statutory employment contributions by firms who employ long-term unemployed people, together with a Fr2,000 a month subsidy for two years on every unemployed person given a job. The package included an index-linked increase in the minimum wage from July 1 - a move that was popular politically, but not obviously designed to reduce unemployment.
The prime minister failed, however, to say what all this extra spending would cost. Nor did he reveal how it would be paid for. Not surprisingly, the markets were not impressed.
The French budget deficit, now running at Fr450bn, or six per cent of gross domestic product, is reckoned to be too high and is not expected to fall substantially over the next few years. Inevitably, the markets were worried that this new spending on cutting unemployment threatened to swell that deficit and encourage inflation. In response, the franc weakened a couple of pfennigs against the mark, to DM3.56.
For the moment, however, the markets are being cautious. They are waiting to see the funding side of the equation, which is likely to be revealed in late June or early July and will probably consist of a mixture of VAT and other tax increases, spending cuts, increased government borrowing and proceeds from privatisation.
It is essential to the French strategy that these measures should be convincing, but at the moment there is considerable scepticism. At worst, a failure to balance spending with new sources of funding would mean the deficit rising to Italian or Swedish proportions.
"I'm not yet persuaded they really want to reduce the deficit by much," said Gwynn Hatch, economist at James Capel, the stockbrokers. "The UK put in place a credible package of tax rises when its deficit rose out of control, but the French have only dabbled with spending cuts, which is less convincing to the markets."
But the markets will have to be convinced if Chirac is to maintain the other plank of his policy - maintaining a strong franc. France's relatively high interest rates and very low inflation have been responsible for maintaining the "franc fort". But these have also contributed heavily to the high unemployment rate. The usual technique for attacking unemployment is to loosen monetary policy by letting interest rates fall. This, however, is not an option for the new French government, because it might undermine the strength of the franc. If the markets start to worry that the deficit is not being reduced fast enough, they will push down the franc still further.
"If the funding package in the next few weeks is not credible, the markets will kill the franc," said Mr Hatch. That could trigger further French interest rate rises, which would push up the unemployment rate in the face of the government's extra spending to bring it down.
Few analysts in the City of London believe the French government can keep up the balancing act indefinitely. The risk premium contained in French interest rates - the fact that they are some three per cent above German rates - shows that most dealers share this pessimism.
The crucial question, however, is which way the French will jump when they do finally have to go one way or the other. Will they opt to placate domestic political opinion and go all out to bring down unemployment, letting interest rates and the franc decline. Or will they stick to the "franc fort" policy and the determination to meet the requirements for joining a single European currency in 1999?
Until this question is resolved, the financial markets are likely to keep testing Chirac's resolve. "Over the next two years or so, there may still be repeated speculative attacks on the franc," commented one analyst.
"If Chirac turns out to be more serious about unemployment than bringing down the deficit, the franc may eventually have to drop out of the exchange rate mechanism."
In other words, the attacks on the franc by the currency markets that were seen before the election are not likely to stop.
In fact, there are reasons for thinking that the new president may eventually decide to abandon his promise to reduce unemployment. France's high rate of joblessness has more to do with underlying structural problems than with the stage it has reached in the economic cycle. For example, thanks to the country's generous welfare system, the costs to companies of employing a worker are more than twice what they are in Britain. This seems to be a major reason for France's relative lack of success in creating new jobs.
Such structural problems require structural solutions, but last week's measures fell well short of anything so radical. The political will to take the necessary steps, such as abolishing the minimum wage, may simply not be there.
In which case, an unequivocal swing towards the policy of maintaining a strong franc at all costs - the single most consistent objective of French politics over the last few years - would seem the inevitable move. This would leave the government free to do whatever was necessary in tightening monetary policy and cutting the deficit to keep the franc on track for merger with the mark in four years' time. It would reassure the financial markets, and the fear that the franc might be forced out of the ERM would vanish.
That outcome is probably still some way off. In the meantime, Chirac looks set for a duel with the markets in which he and the French central bank will try to maintain the franc's value while pursuing policies that should bring it down. And this, as the British learned in 1992, offers a bonanza to the speculators.
Until Chirac decides which way he is going to jump, someone out there is going to make a great deal of money.