In December 2001 in Laeken, State and government leaders from the States members of the European Union have summoned a « Convention on Europe’s future », and have designated Frenchman Valéry Giscard d’Estaing at its head. The aim of the essay is to analyse the powers of this new President, and to draw conclusions concerning the functioning of the Constitution. Valéry Giscard d’Estaing’s wilful attitude, combined with the possibilities of manoeuvre offered by the function’s novelty, has permitted the President to exercise a certain influence : over the composition of the Convention secretariat, the organisation of the Convention’s works, on its « final product » (a constitutional treaty), or even on the evaluation of the existing « consensus » within the Convention. But the different drafts for the text are written at the Praesidium, taking after debates ; the President cannot press his views on the Convention. Several examples can confirm this, whether taken from proceedings (the interior regulation content, the settling of work groups) or from « fundamental » matters (the establishment of a new « Congress of European peoples » and, to a lesser extent, the Union presidency). Studying the Convention Presidency confirms that one must know how to provoke « support coalitions » around one’s positions to win the game within that pitch. –Summary AFRI-2003