Lebanese President Elias Sarkis is planning trips to Washington and Paris to seek help in transforming the Lebanese Army into a force that could enforce domestic tranquility, Lebanese sources said here yesterday.

Sarkis' decision to take the trips appears to reflect a determination to search more actively for solutions to his country's problems. He has been criticized by Western diplomats for playing a passive role as his country is torn apart by warring elements.

Sarkis received a formal invitation Tuesday from French President Valery Giscard d'Estaing to visit Paris, and he is expected in a few weeks. The Lebanese sources said their government views the visit to Paris as an essential prelude to a trip to Washington.

For Sarkis to go directly to Washington to see President Carter without going to Paris first, the sources said, could be interpreted as a move by Lebanon to join the Camp David peace front of Egypt, Israel and the United States.

Putting France - which preserves good relations with both Syria and Iraq - into the picture is meant to soften the impact of Sarkis turning to the United States for support.

Lebanese Foreign Minister Fuad Boutros and the commander'in-chief of the army, Victor Khoury, are now in Paris.

The Lebanese are seeking $375 million to pay for French help in equipping and training the Lebanese Army so that it can neutralize the heavily armed Christians militias. The militias adversaries in the latest round of warfare in Lebanon.

Saudi Arabia is generally expected to be the main contributor. It already contributes $38 million a year to the Arab League force in Lebanon.

The French make clear that they are glad to help but want to be paid. The Lebanese suggest that the Americans are prepared to donate at least some military aid.There is already some U.S. military aid in the pipeline.

In addition to French military instruction in France or Lebanon, the Lebanese say they are particularly interested in getting Jordanian military instructors, who are familiar with U.S. weapons wsystems. More important, the Jordanians have the advantage of being Moslems who are acceptable to both the Syrians and the Lebanese Christians.

The Jordanian Army is widely regarded as the Arab world's best fighting force. It has successfully trained most of the emirate forces along the Persian Gulf.

The Lebanese government has had difficulty getting the other military elements in the country to accept the country's official army as a credible military force.

About half of the army broke into units that took sides in earlier rounds of fighting between the Christians and Moslems. The other half has undergone inteniive retraining.

Lebanese sources said it was notable that only four men out of the 7,000 who have been retrained defected during the recent fighting, despite intense personal and psychological pressure, especially from the Christian militias, to take sides in the defense of their own families and communities. Lebanese sources say however, that they have no illusions that they can create a fully integrated national army divorced form religious and community ties.

One idea is to introduce a universal draft in which the Christian militias could be absorbed as the equivalent of national guard units alongside Moslem-oriented national guards with an intergrated regular army over them at the disposition of the national government.

Once there is a national military structure, Lebanese officials argue, the justification for the presence of Syrians forces to keep order will have been removed. The Syrians first moved into the country when the Lebanese Army disintegrated in the midst of Moslem-Christian Civil War.

Lebanese Christian leaders say they want an army strong enough to keep the peace but not stronge enough to become a n independent political force that might be tempted to take over the country. Breaking it into antional guard and regualr army components could also keep it split up enough so that it would not be tempted to seek political powder.