France took over the EU's six-month rotating presidency this month and in addition to opposing the treaty, many of the protesters were farmers who feel that Sarkozy has failed to defend their agricultural interests.
Six tractors were driven into the city centre to underline their point, with one banner reading: "Mr President, defend farmers and European food."
Ahead of the meeting, Kouchner said: "We are [travelling to Ireland] as the French presidency of the union and not as 'France, the giver of lessons'. We will listen to all sides."
A joint statement after the talks between Cowen and Sarkozy sought to downplay any tensions between the countries, while also clearly signalling Sarkozy's view that the treaty is not dead.
The statement said: "The [French] president confirmed that he respected the outcome of the Irish referendum, but welcomed the fact the ratification process is continuing in other [EU] states and expressed his commitment to the Lisbon Treaty.
"The two leaders undertook to work closely together in seeking a way forward for the union."
Before the meeting, the Irish premier, in an opinion piece in the Irish Times newpaper, gave what commentators said was a message to Sarkozy to back off, and not push too hard for Ireland to decide on its next step.
|Sarkozy sparked outrage by suggesting Ireland should vote again [GALLO/GETTY]
Cowen said: "We need patience and understanding from our partners over the coming months as we complete that process.
"I fully respect the verdict of the Irish people, and I have made that clear to my European colleagues. And I have made clear that I expect them to do likewise."
Ireland was the only EU state to hold a referendum on the Lisbon Treaty, with 53.4 per cent of the population rejecting it.
It is aimed at streamlining the bloc's institutions and needs to be ratified by all countries in the EU to take effect.
EU leaders are set to discuss the crisis again at an October summit, and Sarkozy has set a deadline of the end of this year to overcome the impasse, ahead of elections next year to the European parliament.
Eurosceptics in Ireland and elsewhere claim the treaty is little more than a mildly-tweaked version of the previous EU constitution, rejected by French and Dutch voters in referendums in 2005.
Irish and French government officials have played down the likelihood of concrete developments arising from Monday's meetings.
Declan Ganley, a millionaire businessman and key leader of the Irish 'No' vote, used the visit to highlight his plans to field anti-Lisbon candidates across the EU in the European parliament elections.
Ganley, who says he supports a "strong, prosperous and democratically legitimate" Europe, said he will ask Sarkozy to "accept that the Irish people have rejected the Lisbon Treaty".
He said next June's EU elections should be turned into a "proxy referendum... to make sure that the Lisbon Treaty is not dug up out of the grave that the Irish people have put it in".
A spokeswoman for Sinn Fein, an Irish political party that campaigned against the treaty, said: "There can't be any re-run. A new treaty is required. He [Sarkozy] needs to listen to this."