A French Marine was slightly wounded here today when one of two men riding a motorcycle hurled a grenade at a troop truck as it traveled through predominantly Moslem West Beirut.

It was the second attack on members of the 4,300-member multinational peace-keeping force and came amid other signs of increased violence in Beirut after a period of relative calm.

Since Thursday three other explosions have occurred here. A bomb caused severe damage yesterday to a downtown West Beirut building where the newspaper of an Arab nationalist organization has its offices. The night before, a bomb blasted out windows and walls of an apartment building where two leaders of another such group lived.

No one was injured in either of those explosions, but five persons were wounded when a bomb went off in front of a shoe store in Beirut's main shopping district late last night.

Also yesterday, a blast believed to have been from a car bomb ripped apart a three-story building in the Bekaa Valley town of Shtawrah, 30 miles east of here, where Syrian officers and Palestine Liberation Organization guerrillas had offices. Rescue teams were still digging bodies out of the rubble today. Lebanese civil defense officials estimated that 37 persons were killed, but Shtawrah police said the number of dead was unknown and could be less than half that.

In the Shtawrah explosion, two organizations claimed responsibility, the virtually unknown Front for the Liberation of Lebanon from Foreigners and the Forces of the Cedars.

No group claimed responsibility in any of the other attacks. But the incidents raised fears that Beirut has not yet seen the end of the new cycle of violence.

In barbershops, restaurants and stores those fears were the talk of the day, although they did not disrupt the normal Saturday crowds shopping along the waterfront on a sunny day.

The grenade hurled at the French troop truck was especially worrisome as the assault was the first that unquestionably was aimed at a member of the peace-keeping force.

A U.S. Marine was slightly wounded in November when a car bomb exploded near his position, but the attack might not have been aimed specifically at the Marines. In September, a Marine was killed by the explosion of abandoned ordnance.

U.S. Marines here have kept close to their stations, but French and Italian troops have roamed freely through the city, without incident until now.

Spokesmen for the French 1,650-member contingent said Pascal Garby, a Parisian, was wounded when the antitank grenade hit the back of the troop-carrying truck and exploded. A Lebanese road crewman working nearby was also slightly wounded by shrapnel.

The assailants escaped in the heavy traffic, which a French spokesman said prevented the Marines from using their weapons.

Israeli Defense Minister Ariel Sharon, arguing for a continued Israeli military presence in Lebanon, charged this week that multinational forces here are unable to keep the peace.