Lebanese President Amin Gemayel called today for a U.N.-sponsored referendum to be held in areas of Lebanon under Syrian and Israeli occupation to determine the level of support for his government.

The Lebanese leader was speaking to reporters after a meeting with French President Francois Mitterrand on his way home from consultations in Washington with President Reagan. France, which held a mandate over Lebanon until 1943, is reported to be considering increasing the size of its 2,000-man contingent in the multinational peace-keeping force deployed around Beirut.

Gemayel's plea for a referendum came just 48 hours after the establishment of an opposition National Salvation Front by three Syrian-backed politicians. The president, whose authority up to now has been restricted to a relatively small region around Beirut, told reporters that the referendum would demonstrate the support of the Lebanese people for thelegitimate government.

The leader of the opposition group is Walid Jumblatt, the hereditary leader of the Druze Moslems, whose forces have been engaged in heavy fighting near Beirut with Christian militia units of Gemayel's Phalangist Party. He has enlisted the support of two prominent Lebanese politicians, Christian ex-president Suleiman Franjieh and former prime minister Rashid Karami.

Gemayel first raised the idea of a referendum in the occupied areas shortly after his election in September 1982. He has demanded the complete pullback of both Israeli and Syrian troops.

The unraveling of the agreement for the withdrawal of Israeli troops from Lebanon negotiated by former U.S. special envoy Philip C. Habib has caused concern in France, which is heavily committed to Gemayel's government. French diplomats fear that recent developments in Lebanon could lead to the de facto partition of the country into three zones, with the Israelis in the south, the Christians in the center, and the Syrians in the north and east.

Gemayel said today that the Lebanese Army would be deployed in the Chouf Mountains southeast of Beirut following the withdrawal of the Israelis. The Israelis have announced that they intend to pull back to behind the Awwali River in the south of the country.

French spokesmen have refused to confirm reports from Beirut that an additional 3,000 French troops might be sent to patrol the Chouf following the Israeli redeployment. Last week, however, Foreign Minister Claude Cheysson said France would be ready to consider such a request if there were "a Lebanese government request," "a real need" and the agreement of both Druze and Phalangist factions in the area.

"We are not going to extend the mandate of the multinational force in order to make war but in order to allow the Lebanese Army to keep the peace," Cheysson said in a radio interview.

Cheysson added that any change in the deployment of French forces would also depend on consultations with other members of the multinational force: the United States, Britain and Italy.

In another development,Cheysson flew to Tunis yesterday for talks with Yasser Arafat, leader of the Palestine Liberation Organization.