At least two cheers and a large sigh of relief are in order as the first European peacekeeping contingents set up camp in the Sinai Desert this week. The third, and loudest, cheer must be reserved for April 25, when the Israelis complete their Sinai withdrawal and the Israeli-Egyptian peace finally comes into full force.

The French, Italian, Dutch and British units will be only a part of the Multinational Force and Observers (MFO) painstakingly recruited by the United States under the terms of the treaty. But European participation was critical, not only for the essential breadth and balance it would add, but for its influence on others (the Australians, for example) who, for reasons having mostly to do with Arab oil and markets, were also reluctant to get involved.

So it is worth examining just how hair-raisingly chancy a thing the MFO outcome was--how heated it got, and how close it came to collapsing.

This largely untold story says a lot about the sensitivities and antipathies that will bedevil further efforts to advance the Mideast peace process, about the state of working relations in the Atlantic alliance--and about the wrath of Alexander Haig. If you've been wondering, for example, what gave rise to a particularly titillating tidbit in those notes of Haig's staff meetings published by The Post--the one that has him calling his British opposite number, Lord Carrington, a "duplicitous bastard"--well, stay tuned.

The problem really traces back to two flaws in the Camp David Accords. One was its prescription for a United Nations peacekeeping force, which was never in the cards simply because the Soviets would have vetoed it. A fallback position, attached to the accords, was a promise by Jimmy Carter to Egypt and Israel that the United States would mobilize a multinational force.

But recruitment was confounded by a second flaw: the exclusion from Camp David of the rest of the Arabs, notably the oil producers, and their consequent condemnation of all its works. To the Saudis, for one example, anybody participating in the Sinai peacekeeping force was guilty, by even that much association with Camp David, of a "provocative" act.

So when they were approached by the United States last year, the four European candidates weighed their oil and commercial interests in the Arab world, and hedged their agreement to participate. By way of spreading the risk and strengthening their political base, they insisted on first getting a go- ahead from all of the Common Market's 10 members. Their notion of a proper resolution of the Arab-Israeli dispute is markedly sympathetic to the Arab side--and an anathema to Israel.

As expressed in the famous Venice Declaration of the Ten in June 1980, it dwells heavily on the "rights" of the Palestinian people, promises them "self- determination" and insists that the Palestine Liberation Organization be "associated" with negotiations on a settlement.

The upshot of the Common Market deliberations was agreement on careful wording of a letter that the French, British, Italians and Dutch would deliver to the Israeli and Egyptian governments. The effect was to link their participation in the MFO to the terms of the Venice Declaration.

But even that was not good enough for the jittery British. "They wanted a way out," says one allied diplomat closely involved. To that end, the British reportedly gave the State Department a particularly hairy account of Saudi threats of reprisals--one that did not match what the Saudis were conveying to Al Haig. This was the "duplicity" that Haig was hanging on Carrington.

But that may not have been Carrington's worst offense in the eyes of Haig and some of the European partners. As chairman of the Ten, it was left to him to advise the United States of the terms of the letter of acceptance of the four European countries. Subsequent events suggest that whatever sense of it he conveyed was inadequate.

So it was that on Nov. 9 last year, just one day before the letter was to be delivered, Haig first saw a copy, courtesy of the ever-resourceful Israelis. The Israelis were outraged: it was an "unacceptable" departure from Camp David; they would exercise their right to veto European participation. As for Haig, "he was livid" (says a European in a position to know). It took a flurry of florid phone calls to put the letter on hold.

On Dec. 4, after days of three-cornered, hot and heavy remedial diplomacy, a masterpiece of papering-over produced a joint U.S.-Israeli statement reaffirming Camp David. It took pointed note of "clarifications" received from the four European participants that "they have attached no political conditions, linked to Venice or otherwise."

Success? Yes, but also a reminder of the deeply divergent forces at work against even such an upbeat piece of Mideast peacekeeping as the policing of the Sinai Desert against renewed hostilities.