Abbas heads to Washington in an attempt to try to turn Israel's withdrawal from the Gaza Strip into a springboard for resurrecting negotiations between Israel and the Palestinian Authority.
The visits are part of a five-nation tour by the Palestinian leader, which began over the weekend when he visited Jordan and Egypt. He will also travel to Spain before heading to the US midweek.
His trip to Europe and the United States will be the first time Abbas has left the Middle East since Israeli soldiers withdrew from the Gaza Strip on 12 September - a move the international community hopes will revitalise the ailing peace process.
During the Paris talks, Abbas will ask that France "continue to play a positive and effective role within the European Union in support of the Palestinian cause and peace process aimed at reaching a true settlement", Palestinian Foreign Minister Nasser al-Qidwa said.
Chirac (L) is said to be playing a
positive role in the conflict
"Our relations with Europe, and particularly with France, are very important, and we are always trying to strengthen them," added al-Qidwa, who will accompany the Palestinian leader on his tour.
Abbas is to hold talks with French President Jacques Chirac on Monday and Foreign Minister Philippe Douste-Blazy on Tuesday.
Although France is a traditional ally of the Palestinians, Abbas will also raise Palestinian concerns about the involvement of two French firms in a tramway project that will pass through two settlements in occupied East Jerusalem, the minister said.
Al-Qidwa said he was "deeply worried" by the involvement of Alstom and Connex, the transport arm of the French conglomerate Veolia, in the tramway project he said contravened international law.
Fate of Gaza
On Tuesday, Abbas will hold talks in Madrid with Spanish Prime Minister Jose Luis Rodriguez Zapatero and Foreign Minister Miguel Angel Moratinos, before arriving in Washington on Wednesday ahead of his second meeting with US President George Bush.
Abbas will urge US to pressure on Israel to settle "the unresolved issues" linked to the Gaza pullout, al-Qidwa said.
Topping the agenda is the fate of Gaza's air and sea ports, removal of the rubble from the demolished Jewish settlements, and the Rafah border crossing with Egypt - Gaza's only access to the rest of the world - which has been closed since 7 September.
"We will focus on Gaza after the withdrawal... We will also demand a halt to settlement activity and construction of the wall in the West Bank"
Palestinian foreign minister
"We will focus on Gaza after the withdrawal. We want to see similar steps in the West Bank as well as implementation of the road map," he said.
The road map is a peace blueprint for the creation of an independent Palestinian state, backed by the UN, Russia, the EU and the US.
"We will also demand a halt to settlement activity and construction of the wall in the West Bank," al-Qidwa added, referring to Israel's vast separation barrier snaking across the territory.
Abbas will resist US pressure to exclude the Hamas resistance movement from participating in Palestinian legislative elections in January, al-Qidwa added.
Top Abbas spokesman Nabil Abu Rudaina said the Palestinian leader will update Bush on the situation in the Gaza Strip since the pullout.
"We will show Bush the steps we have taken since the Israeli withdrawal from Gaza and the obstacles which we are facing," he said.
"Gaza alone is not enough. It is one step forward but we have to build on this," he added.
"Contact between the Palestinians and the Israelis must be renewed at the level of serious negotiations about implementation of the road map and about the creation of a viable and contiguous Palestinian state of which Bush has spoken," he added.
The Palestinians will ask for "swift measures" to maintain the momentum created by the Gaza withdrawal, including "the release of prisoners held by Israel, the removal of checkpoints, the end of settlement activities and a solution to ensure the Rafah crossing is reopened", he said.