Heavy rocket, mortar and artillery duels raged unchecked between Syrian troops and Christian forces in Beirut yesterday and shelling spread for the first time to the predominantly Moslem western half of the city.

The presidential palance on hills east of the city was hit along with an adjacent barracks by a dozen mortar rounds, wounding seven palace guards, witnesses said.

President Elias Sarkis was uninjured and later headed a Cabinet session trying to find a way out of the increasingly large-scale clashes between Christian militias and the 30,000 Syrian soldiers occupying Lebanon as the backbone of a pan-Arab peacemaking force.

In a reflection of Western concern that the Lebanese fighting could undermine the Camp David peace agreements, the French government announced that President Valery Giscard d'Estaing had contacted Sarkis by telephone about a French ceasefire proposal.

French Foreign Minister Louis de Guiringaud began the French effort Tuesday at the United Nations, concentrating on redeployment of the Syrian troops in Beirut. The French idea drew a negative initial reaction from Syrian President Hafez Assad, who called it "strange," but U.N. diplomats were still awaiting a formal Syrian response.

Casually figures were unavailable in Beirut in the chaos of combat. The Voice of Lebanon, the radio of the rightist Christian Phalange Party, estimated more than 500 persons were killed in the last 24-hour period, most of them civilians caught in the shelling.

"We are still under Syrian volcanoes," the Phalange radio said. "Beirut is like a military island surrounded by smoke, flames and destruction - isolated from the whole world, where there is no water, electricity, transportation, medicine or food supplies."

The Phalange militia is the largest of the Maronite Christian irregular forces battling Syria's peacemaker troops. Legally, the Syria forces are under Sarkis' command to enable him to rebuild state authority demolished in the civil war that has raged off and on in Lebanon since April 1975.

For the first time since the current round of Syrian-Christian strife erupted in February, shelling spread into the largely Moslem western sector of Beirut. Previous exchanges were restricted to the predominatly Christian eastern quarters, particularly the Maronite Christian enclave of Ashrafiyeh.

The shells crashing into western Beirut knocked out electric power, plunging the city into darkness Tuesday night and cutting telephone and telex connections with the outside world. There was no way to tell with certainty from Syrian or Christian artillery.

Leftist Lebanese militiamen threw up roadblocks to protect their strongholds in the western party of the city and began checking identification cards of passing motorists, as they had for months during the first phase of the civil war before Syrian occupation. But there was no sign the Moslem leftist or their Palestinian guerrilla allies were taking part in the current fighting.

Aside from the long-distance shelling, the largest concentrated battle appeared to center on Christian efforts to dislodge Syrian troops from a key bridge on the seaside road leading north from eastern Beirut toward the seaside resort town of Jounieh and, beyond, to the Mount Lebanon area known as to the ancestral Maronite Christian heartland.

A fire raged out of control at an oil storage depot on the northeastern fringe of the city for the second day running, putting a black shroud over the embattled eastern quarters.