In 1986, the last time France had a cohabitation government, he said he would invite the head of the largest party in parliament - then Jacques Chirac, leader of the Gaullist RPR - to form a government.
If Mr Mitterand were to follow that formula again, Mr Chirac would again be on the point of taking over the Hotel Matignon, the prime minister's residence. But Mr Chirac, preferring to concentrate on his own campaign for the presidency in two years' time, has said he is not a candidate. The leading contender is Edouard Balladur, 63, who was finance minister in Mr Chirac's last government. He has a courtly manner, is respected by the President and is unlikely to ruffle him unduly.
Unless the many behind-the-scenes consultations between the Socialist President and the victorious conservatives have established another formula, it is likely that Mr Mitterrand will call in Mr Chirac for consultations and then quickly move to name Mr Balladur, almost certainly on Tuesday. Then, the resignation of the Socialist government of Pierre Beregovoy can take effect. Mr Balladur is reported to have drawn up his list of ministers already and could announce the cabinet's composition on Wednesday or Thursday. The first cabinet meeting is already tentatively scheduled for Saturday.
But really hard times for Mr Mitterrand will begin on Friday - when the National Assembly opens its first session of the five-year legislature, with at least 100 newly elected members. Calls on Mr Mitterrand to assume responsibility for the Socialist defeat and leave office can then be expected to amplify.
Mr Chirac rocked the Elysee Palace last week by remarking that Mr Mitterrand should go. Supporters of the President said he might appoint a prime minister from the Gaullists' centre-right ally, the Union for French Democracy (UDF), rather than from a group which was calling for his retirement. If the President does this, the most likely candidates would be Valery Giscard d'Estaing, the former president whom Mr Mitterrand defeated in 1981, or Francois Leotard, who was culture minister in the last cohabitation.
Presiding over his last meeting with a Socialist cabinet last Wednesday, Mr Mitterrand, 76, said that only ill health would make him leave office before his seven-year term ends in 1995. He was found to have cancer of the prostate last September, and could play the health card any time.
There is no doubt there will be a clamour for the President to go. The prospect of a five-year presidency, first raised by Georges Pompidou 20 years ago, was revived by Mr Mitterrand during his second mandate. The opposition welcomed this and suggested he apply it to himself - meaning that he would leave office in May this year. Then he dropped the project from proposed institutional reforms.
Mr Giscard d'Estaing, Mr Chirac's main conservative rival for the presidency, has said he will push for a five- year mandate. This campaign is likely to find favour among supporters of the new government. It would have the permanent merit of enabling new presidents and the lower house of parliament to be elected simultaneously, eliminating future cohabitations.
By tradition, but not under the Constitution, the President, who is chief of the armed forces, retains control of foreign affairs and defence.
In 1986, when the right had a slender five-seat majority, Mr Mitterrand could impose his choice of defence and foreign ministers. This time, the government will be less co-operative with him. The most probable defence minister is Charles Pasqua, the head of the Gaullist group in the Senate and a blunt critic of Mr Mitterrand. The Foreign Ministry is likely to go to either Alain Juppe, the Gaullist secretary-general, or Mr Leotard.
It is here, however, that the conservatives most fear clashes with the President. In the last cohabitation both the President and the prime minister attended European and Group of Seven summits, for example. This time, the parliamentary majority will certainly be hostile to Mr Mitterrand presenting himself abroad as the voice of France.
France's former foreign policy 'consensus' is a dead letter after the collapse of Communism in Europe. With 35,000 soldiers abroad, in former African colonies or on United Nations peace-keeping missions from Bosnia to Cambodia, differences in this domain could be explosive.
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