President Reagan has picked an old friend with no foreign affairs experience for the No. 2 job in the State Department -- a man Secretary of State Alexander M. Haig Jr. initially did not want as his deputy, but now endorses warmly.

William P. Clark, 49, a justice of the California Supreme Court (Reagan gave him the job), was backed for the State Department post by members of Reagan's inner circle, especially White House counselor Edwin Meese III. According to informed sources, Meese thought the new president needed a totally loyal friend at the State Department to keep an eye on Haig.

Haig announced yesterday that he had given his "enthusiastic endorsement" to the selection of Clark, whom Haig called "a superb choice." Just two weeks ago, however, aides to the new secretary told reporters that Haig hoped to head off Clark's appointment.

These aides said confirmation hearings for Clark as deputy secretary could prove embarrassing because of Clark's inexperience, and because he had failed to finish college and flunked out of law school as a young man.

In the last two weeks Haig and Clark have had at least two long conversations.

Some of Reagan's closest associates disagreed with Meese that Clark should go to the State Department, according to reliable sources. These associates thought Clark would do better somewhere else in the government, the sources said.

Clark began a round of meetings with members of the Senate yesterday. According to several Senate sources, Clark openly discussed the fact that he had no experience in foreign affairs, and dwelt on his abilities as an administrator. It was administrative skills that made Clark a valuable right-hand man to Reagan during his first term as governor of California.

One Senate source who took part in one of Clark's meetings on Capitol Hill yesterday said Clark had made a poor impression. "I thought he was awfully weak. He seemed uncomfortable," this source said.

But an aide to a Democratic member of the Foreign Relations Committee said he saw little likelihood that Clark would have trouble winning Senate confirmation.

"The guy has certainly had an undistinguished educational record, to say the least," this aide said. "But pinning a 'no' vote on his record would be hard. . . . After all, Harry Truman never went to college."

The White House decision to install Clark at Haig's side on the seventh floor of the State Department is the first example of a senior appointment in the administration that was clearly initiated by the president rather than his Cabinet officer. Sources close to Reagan have said all along that he would be making such appointments in some key jobs below the Cabinet level.

Haig has assembled a team of top assistants who clearly are his own choices.

Most of them are Foreign Service officers Haig knew from his service in the Nixon and Ford administrations or while he was supreme commander of NATO forces in Europe.

Sen. Jesse A. Helms (R-N.C.) and other conservatives have expressed displeasure at some of Haig's reported choices (they have not been formally nominated to their new jobs).

Bureaucracy-watchers may perceive something of a trade between the Clark appointment and the previously revealed selection of two military men who are both Haig proteges in the upper reaches of the National Security Council staff in the White House.

Haig has said that he intends to be unmistakeably the lead official on foreign policy in the Reagan administration, and the choice of his proteges for those NSC jobs reinforces his claim to preeminence.

As it turns out, the Reagan inner circle will now be represented next to Haig in the State Department, and Haig will be represented next to Reagan's national security affairs adviser, Richard V. Allen, in the White House.

In 1970, when Clark had to be chosen by the voters to retain his seat on the state superior court, the first judicial post to which Reagan appointed him, Clark's campaign literature said that he "earned his way through college and law school."

A campaign biography listed Stanford University and Loyola Law School under the heading "educational." But Clark never completed his studies at either institution, and had to withdraw from Loyola, an evening law school, because of poor grades.

California regulations enabled Clark to take the state bar exam without a degree from law school. The first time he took the exam he failed. He passed on the second attempt.