Lebanese Foreign Minister Elie Salem said yesterday that France has agreed to increase its troop contribution to the multinational peace-keeping force in Beirut if the United States and Italy do the same. He asked Washington and Rome for a "commitment in principle" to enlarge the force eventually.

Salem, speaking at an American Enterprise Institute luncheon, said French Foreign Minister Claude Cheysson had told him in Paris Saturday that France is ready to accede to the Lebanese government's request for more troops "in conjunction with the other countries now participating in the MNF [multinational force]."

Lebanon, the minister continued, is asking the United States and Italy to commit themselves to increasing and redeploying the force when agreement is reached on withdrawal of foreign forces from his country. He said an advance commitment is necessary so changes in the force's strength and mission can be accomplished "at very short notice, no more than a week."

The force has about 1,200 U.S. Marines, 1,600 French troops and 1,000 Italian troops.

Lebanese President Amin Gemayel has asked that the force be increased, but the Reagan administration has said it does not want to make a decision without a clearer picture of security problems Lebanon might face after a withdrawal agreement.

Salem acknowledged that if Israeli, Syrian and Palestine Liberation Organization forces withdraw, there will be a period, "until such time as the Lebanese Army is built up," when the Gemayel government will require the aid of an outside force numbering 15,000 or more.

He said that training Lebanese military and security forces to assume full control of the country "should not take very long."

However, most outside estimates, including those of Pentagon planners, say that will take about two years, and the administration is concerned that an increased U.S. commitment for that long could provoke opposition from Congress.

Salem charged that the main bar to starting withdrawal talks has been Israel's demand for negotiations in Jerusalem and a security agreement that could be construed as a peace treaty.

To accede to these conditions, he said, would jeopardize Gemayel's support at home and in other Arab countries.

He acknowledged that one idea being considered to overcome this hurdle calls for special U.S. Mideast envoys Philip C. Habib and Morris Draper to shuttle between Israel and Lebanon as intermediaries. "There are many possibilities, and we are investigating all of them," he said.

The State Department, saying that it is time for "quiet diplomacy," said yesterday that it is putting a clamp on public discussion of the Habib and Draper mission.

In response to questions about the future of Palestinians in Lebanon, Salem said that the 238,000 there as legally registered residents can remain but that his government wants thousands of others, whose presence it considers illegal, to leave. Asked where they might go, he said:

"All illegals legally belong someplace else."