Fierce fighting broke out today between Moslem militiamen and Lebanese Army soldiers in the no man's land dividing the Moslem and Christian sectors of Beirut as the final French contingent of the international peace-keeping force prepared to leave.

The four-hour battle, the most severe since the international force came to Lebanon to oversee the evacuation of Palestinian guerrillas last month, caught a French Army convoy ferrying supplies to the port, setting off the explosion of one of its ammunition trucks and burning two other vehicles but causing no casualties.

The outbreak of fighting in Beirut came as Israel said its warplanes destroyed another Syrian antiaircraft missile site in central Lebanon and the Israeli Cabinet warned Syria that it would not tolerate continuing cease-fire violations. Israel also announced that three of its soldiers were killed by artillery fire in central Lebanon on Friday.

The French withdrew from today's attack in downtown Beirut without firing a shot, under a barrage of machine-gun fire and rocket- propelled grenades that whistled over their heads.

The battle, in the Ras Nabeh neighborhood near the recently reopened Sodeco crossing point between the city's two sectors, increased fears here that with the withdrawal of the international force the tenuous peace that followed its arrival last month might collapse.

Observers were encouraged, however, that the Lebanese Army, which has been deployed in positions previously occupied by Palestinian fighters around Israeli-besieged West Beirut, weathered its first real test of fire since being reconstituted as a force three years ago. The Army disintegrated in 1976 at the height of the Christian-Moslem civil war.

Lebanese national television reported that one soldier was killed and 13 wounded in the firefight through the neighborhood of shell-pocked buildings destroyed seven years ago at the outbreak of the civil war.

The television also said an undetermined number of militiamen, from a leftist group known as the Partisans of Revolution, were killed and injured. Two civilians were reported killed by stray bullets.

There were conflicting reports of how the battle began. Army sources and the national television said it started when a member of the Partisans of Revolution, which has long controlled the area around the Sodeco crossing, opened fire on a convoy of cars carrying Moslem politicians to the Christian town of Bikfaiya to meet with President-elect Bashir Gemayel. Beirut's many Moslem factions bitterly opposed the election last month of Gemayel, a leader of the Christian militias that they fought during the civil war.

According to the Army source, a squad of national policemen, who have been charged with reestablishing government authority in West Beirut for the first time in seven years, arrested the man who fired on the convoy. But before they could take him from the area he was freed by other members of the leftist group, the source said.

The Army was then called in, with armored vehicles and trucks mounted with heavy machine guns, setting off the battle that raged for four hours. Scattered shooting continued long after dark. Rocket-propelled grenades fired into militia positions in an apartment set the building afire, sending up a black plume of smoke.

Prime Minister Shafiq Wazzan, who has been instrumental in negotiating with Beirut's Moslem leaders to persuade them to allow the police -- backed in emergencies by the Army -- to assume control of the city, went on television tonight to urge everyone to back the Army, which Moslems have accused of being an instrument of their Christian enemies.

The fight in Beirut almost eclipsed continuing tension along the cease-fire lines betweeen Israel and Syria in the mountains east of the Lebanese capital, along the Beirut-to-Damascus highway.

For the third time in a week Israeli jets attacked Syrian SA9 ground-to-air missile batteries near Dahr al Baydar, six miles beyond Israel's positions around the village of Bhamdun. In the same area last week, a unit of the Palestine Liberation Organization captured eight Israeli soldiers now being held prisoner.

Israeli military spokesmen reported in Jerusalem that the air raid today knocked out another of the four-missile SA batteries, bringing the total destroyed in the past week to six.

The attack came as the Israeli Cabinet again warned Syria that it would not tolerate continuing cease-fire violations in Lebanon. The remarks had been prompted by the capture of the eight soldiers and the ambush in the area Friday of an Israeli Army jeep that killed three Israeli soldiers and wounded one.

Israeli Cabinet spokesman Dan Meridor warned after the meeting that Israel would accept neither continuing cease-fire violations nor a long war of attrition in Lebanon.

Syria is reported to have 25,000 soldiers in the area and the PLO as many as 10,000, including many who withdrew from Beirut last month under the provisions of an accord worked out by U.S. special envoy Philip C. Habib.

U.S. and Italian troops of the international peace-keeping force that oversaw the withdrawal left Lebanon last week. France is preparing to remove its troops this week despite requests by the Lebanese government that they stay.

The French convoy that got caught in the fighting today was one of the first moving its troops and supplies from their positions along the crossing points in the heart of the city, to the port of Beirut from where they are to depart Tuesday.