A month ago, he was thought to have no chance of winning a snap parliamentary election which had caught his Socialist Party ill-prepared (just as President Jacques Chirac had intended it would).
Last night, Mr Jospin, 59, was Prime Minister-elect. President Chirac's strategy, and his presidency, were in ruins. France faced five years of left-right power-sharing, or "co-habitation", in which Mr Jospin, as leader of the parliamentary majority, will have the whip's hand.
How did Mr Jospin do it? In all truth, he didn't; the victory, to a large extent, fell into his lap. The Socialist leader has once again proved an energetic and able campaigner. But his main achievement in the past few weeks has been to offer a likeable and competent alternative to an inordinately unpopular government running a desperately incompetent campaign.
There is no clear decision by the French people to turn to the left; there is no wide, popular enthusiasm for, or confidence in, the Socialist party, and certainly not in its Communist allies. In the first round of the election, the two political formations in the centre-right government attracted less than one in four of the possible voters. But the Socialists and the other left-wing parties attracted the votes of just over one in four of the potential electorate. This is the lowest first-round support for the ultimate governing parties in nearly 40 years of the Fifth Republic.
There was a clear rejection last night of the deflationary policy of the centre-right government, which put the shrinking of the welfare state and the private sector, and the creation of the European single currency, ahead of tackling unemployment. President Chirac promised to do the opposite when he was elected two years ago, and has paid the price.
The striking fact is that the French electorate has turned out its government (but not its President) at every opportunity it has been given to do so in the past two decades. The last time a French parliamentary majority was re-elected was in 1978. In the five parliamentary elections since then, France has moved left, right, left, right and then left again. No other country in Europe has such a record of political fractiousness, or, increasingly it has to be said, contempt for politicians of all persuasions.
Mr Jospin can look forward to five years in power. But, unlike Tony Blair in Britain, he does not inherit a benign economy. With unemployment at 12.8 per cent and growth stuttering, he has little room for manoeuvre. The outgoing government had placed all its bets on the medium and long- term benefits of tax cuts, and a strong single currency. Mr Jospin's prescriptions are mostly short-term: government action to create 700,000 jobs for young people, half in the state sector, and a gradual move to a 35-hour week without loss of pay. A Jospin government will continue some of the state- shrinking reforms begun by Prime Minister Alain Juppe's ill-fated government, and quietly abandon others. There is little here to improve France's long- term competitivity.
And what of the single currency? It now seems impossible that the euro will arrive both strong and on time. Mr Jospin campaigned for a more relaxed interpretation of the Maastricht guidelines for Economic and Monetary Union (Emu). He is not prepared to impose further short-term budgetary or fiscal pain on the stuttering French economy to meet the Emu targets. He is not prepared to join a single currency which excludes Italy and Spain, possibly placing French farmers and manufacturers at a competitive disadvantage.
It is clear that the mood of the French people backs Mr Jospin rather than the old policy of Emu-or-bust. But the single currency, if it is not to be a disaster on birth, has to meet the test of the international bond markets (something Mr Jospin prefers to forget).
With a single currency civil war still raging in the German establishment, the advent of the Left in France may provide an opportunity for some sort of global Emu compromise; or it could derail the euro altogether.
The great unknown is how President Chirac will take to co-habitation and whether he will survive it. On the surface, there is no reason why he should not rub along as well as President Mitterrand did. Mr Chirac is a clubbable man and a man without a fixed ideology. He should manage, as Mitterrand did, to co-exist with the opposition, while trying to trip them up when he can. The uncertainty comes from the tangle of investigations under way into the dubious finances of his RPR party. Without centre-right hands on all the levers of power, one or two of these investigations might come uncomfortably close to the President himself.