"We want the European Union to have a political role that complements the role of the quartet in the region."
Abbas said: "We will work with anyone the Israelis choose, but on the condition that they don't bring us back to the starting point. There will not be other opportunities to make peace in the Middle East if we let this moment pass.
"This is why we are telling anyone who could be the next Israeli prime minister, in the same way as we are telling President [Barack] Obama and President [Nicolas] Sarkozy, that this is an opportunity that we cannot miss."
Abbas, a member of Fatah, is at the start of a European tour which will include visits to Britain, Italy, Turkey and Poland.
Kouchner said Abbas had discussed working with Hamas, Fatah's rival Palestinian faction, during their talks.
The foreign minister said: "The president and I talked about the Palestinian reconciliation and that is a major issue, that would leave open the possibility to find an agreement to work out a Palestinian unity government to be put in place.
"First of all, in Gaza, the gates must be opened. The checkpoints must be opened. This is not sufficiently the case right now."
Abbas said: "As you know, this reconciliation [with Hamas] is based on two essential principles. A national unity government whose formation will not lead to a blockade.
"A national unity government that considers itself bound by international legality and previous agreements.
"If Palestinian reconciliation is achieved, if the US administration is ready for work and the Israeli government is formed in a short period, I believe that the conditions would make it possible for the political process."
Nour Odeh, Al Jazeera's correspondent in the Palestinian West Bank, said that Abbas "wants European assurances that they will deal with a Palestinian government of national unity that will include Hamas, no doubt, if and when that government is formed.
"In 2007, the Europeans did not agree to deal with a government of national unity headed by Hamas. So Abbas does not want a repeat of that.
"He is telling the Europeans that it is simply unacceptable for them to adopt that same position because it literally jeopardises the future of Palestinians and their aspirations to unite."
Abbas also met with Sarkozy, the French president, and Bernard Accoyer, the president of the lower house of France's parliament.