The main effect was to draw attention away from the succession to the President. While all eyes were on Mr Mitterrand, the battle to replace him - which may now come sooner than planned if he decides he cannot continue until the end of his mandate next May - receded into the background.
In what Raymond Barre, the former centrist prime minister and a perpetual presidentiable (a pretender to the presidency), dismisses as 'the microcosm' - the Parisian salons where the political classes chatter - the talk was that Mr Mitterrand, who will be 78 next month, could well leave the Elysee Palace by Christmas.
Constitutionally, what would happen next is clear cut and well tested. Twice before, when Charles de Gaulle resigned in 1969 and Georges Pompidou died in office in 1974, France was launched into an unexpected presidential campaign. Twenty years ago, it took barely six weeks from Pompidou's death for the two- round presidential election to be organised and for Valery Giscard d'Estaing to be installed as his successor.
This time, the President's departure would be easier to manage since it would merely bring forward a scheduled election by a few months. The names of the main contenders are already well known.
If Mr Mitterrand did go, he would be replaced in the first instance by the President of the Senate, Rene Monory, a former centrist finance and education minister; he would hold the reins until the election. Obligingly, Mr Monory said on Friday that he was 'psychologically ready' to stand in.
Given the political make-up of France at present, the next president should logically come from the right. The conservative coalition of the Gaullist RPR and the centre-right Union for French Democracy (UDF) together have 80 per cent of the seats in the National Assembly, the lower house of parliament, and the government of Edouard Balladur, elected 18 months ago, remains popular.
However, the right lost the last two presidential elections, in 1988 and 1981, in part because it put up two candidates each time. Jacques Chirac, RPR president and Mayor of Paris, stood for the party in 1981, and Giscard d'Estaing, the outgoing president, for the UDF; in 1988, Mr Barre ran for the UDF alongside Mr Chirac.
This time, there could be two candidates from the RPR alone. Mr Chirac has all but declared his candidature while Mr Balladur, riding high in the opinion polls, would be the favourite to win. For many commentators, his candidature is a foregone conclusion.
But the RPR grass roots are a contrary lot, and their preference could well be Mr Chirac, in whom they recognise more of the social awareness and earthiness that they expect from the heirs of De Gaulle.
The Gaullist legacy is seen as a mixture of conservatism and state control (it was he who, after the Second World War, set about nationalising the banks that Mr Balladur has been busy privatising) an obstinately independent foreign policy and social policies to help the underprivileged.
Mr Balladur, with his Savile Row suits and haughty manner, is seen as more aristocratic than Mr Chirac - even technocratic, a Gaullist insult for those functionaries who lack the common touch.
If they both ended up in the running, the way could be open to the left, particularly if the Socialist Party can persuade Jacques Delors, the outgoing European Commission President, to be its candidate.
Until now Mr Delors has hedged his bets, waiting to see precisely what the conservative line-up is likely to be. In private, he is reported to have said: 'Why should I stand against Balladur when I approve of his policies?'
Elsewhere in the conservative field, Mr Barre made noises last week suggesting that he might be a candidate; and Mr Giscard d'Estaing has never abandoned the hope that he may one day regain the Elysee.
Philippe de Villiers, whose maverick anti-Maastricht right- wing list took 12.5 per cent in last June's European election, resigned from the UDF on Friday, and said he might stand. In addition, Jean-Marie Le Pen of the National Front is a certain candidate, though his likely 10 per cent first-round score will be counter-balanced by a similar Communist showing.
A handful of opinion polls have shown that Mr Delors would probably beat Mr Chirac. Another scenario favourable to Mr Delors would be a bruising Balladur-Chirac duel in the first round of voting - due on 23 April.
Even if the Prime Minister did go through to the second round on 7 May, when traditionally the first-round winners of each camp face each other, the damage done to the Gaullists' image could tip the balance in Mr Delors' favour.