Foreign Minister Tzipi Livni is expected to meet with senior French government officials in Paris later this week.
State officials confirmed that the French president plans to lead a move for a 48-hour ceasefire. It is unclear whether Sarkozy or Kouchner will also be meeting with Hamas members.
European foreign ministers called on Tuesday for an immediate and lasting ceasefire between Israel and Hamas and for humanitarian aid to be delivered to Gaza.
The European Union said in a statement after a meeting of foreign ministers in Paris called to discuss the violence that food, medical aid and fuel should be delivered to Gaza, those injured in Israeli military action should be evacuated and humanitarian workers should be allowed access to the area.
"There must be an unconditional halt to rocket attacks by Hamas on Israel and an end to Israeli military action," the statement said.
It also called for a return to the peace process interrupted by Hamas rocket attacks and Israel's retaliatory air strikes. "There is no military solution to the Israeli-Palestinian conflict, in Gaza or elsewhere," the statement said.
'Urgent need to continue on road to peace'
Earlier, foreign ministers from the Quartet of Middle East peace brokers called for an immediate ceasefire in Gaza and southern Israel, a UN spokeswoman said.
The call followed telephone consultations by the officials of the Quartet - grouping the United Nations, the United States, Russia and the European Union - on four days of Israeli air strikes on Gaza responding to Palestinian rocket attacks on Israel.
US Secretary of State Condoleezza Rice, Russian Foreign Minister Sergei Lavrov, UN Secretary General Ban Ki-moon and EU foreign policy chief Javier Solana were on the conference call, UN officials said.
After discussing the situation in Gaza and southern Israel, "They called for an immediate ceasefire that would be fully respected," UN spokeswoman Marie Okabe said.
"They called on all parties to address the serious humanitarian and economic needs in Gaza and to take necessary measures to ensure the continuous provision of humanitarian supplies," she said.
"They agreed on the urgent need for Israelis and Palestinians to continue on the road to peace," Okabe added in what was described as a "readout" of the Quartet discussions but not an official statement by the grouping.
The French mediation initiative for a ceasefire joins additional initiatives aimed at ending the fighting, the main one being led by Egypt. The government in Cairo is in daily contact with senior Defense Ministry official Major-General (Res.) Amod Gilad.
A number of European leaders and foreign ministers are expected to visit Israel in the coming days in a bid to help restore a truce. According to estimates, pressures on Israel to halt its military operation will increase in the coming days.
Reuters contributed to this report