Although it had been long planned, the encounter signalled the intention to mend fences and amounted also to mutual recognition that France had won a foothold, however small, in the US-dominated Middle East peace process.
In another move that may have been designed to improve France's image in Israel, Mr Peres said France recently broke up a group, linked to the Iranian-sponsored Hizbollah organisation, that was planning attacks on Israeli targets in Paris. Neither Israeli nor French officials would confirm this or give details. Until that disclosure on Monday, recent exchanges had been cool. Israeli ministers were less than accommodating to Mr Chirac's special envoy and Foreign Minister, Herve de Charette, during his 12-day Middle East shuttle.
On arrival in Tel Aviv, he was told it was "too early" for a peace mission; as he arrived for a second attempt, officials said there were too many people involved in too many initiatives.
Mr Chirac's visit to Lebanon last month, when he had called for a "free and independent Lebanon", the strength of French condemnation of Israeli action in southern Lebanon, including the shelling of Qana, and the speed with which Mr Chirac sent Mr de Charette to Lebanon in a peace initiative - later scaled down to a "goodwill mission" - all predisposed Israel to regard France as ill-equipped to play the role of honest broker.
Now that France has a place alongside Syria, Lebanon and the US in the "surveillance group" set up to guarantee the ceasefire in southern Lebanon, both have an interest in restoring some civility. France was also gratified by the response of Lebanon, whose President, Elias Hrawi, stopped in Paris on Tuesday and paid tribute to France's role and to Mr Chirac in particular for his "courageous initiative".
The visits by Mr Hrawi and Mr Peres on successive days and within less than a week of the truce agreement allowed officials and commentators to speak of a return of France to Middle East diplomacy, where it regards its ties with Lebanon and its channels to Syria - and to a lesser extent Iran and Iraq - as unique assets.
While France conceded that US mediation was always going to be essential to any truce deal, Mr de Charette insisted on his return that "80 per cent of the text of the ceasefire agreement derived from ideas set out by France from the beginning".
This, however, is not the official US view, or at least not the view being presented for domestic pre-election consumption in Washington.
On Tuesday the US State Department spokesman, Nicholas Burns, rebutted France's claim of an "80-per-cent" contribution. "It is perfectly clear to all those who travelled with the Secretary of State," he said, "that the great success of the ceasefire accord is largely due to the American initiative. The text of the negotiation document was drawn from an American draft; the ideas were American ideas."
Officials in Paris and Washington have denied reports of friction between Mr de Charette and the Secretary of State, Warren Christopher, during their peace missions, insisting that they were in close contact throughout and effectively working together.