President Reagan's multipurpose trip to Europe may cost more than $12 million when all bills are paid for the entourage that the administration has taken along to Paris, Rome, London, Bonn and Berlin.

The U.S. Embassy roster here lists 247 Americans in the Reagan party scattered among 11 different hotels where the rate ranges from $120 to $250 a day. The roster--which includes Nancy Reagan's hairdresser, Julius Bengston--listed every American traveling with Reagan in France except for the president and the first lady, but the total number of Americans involved in the 10-day trip probably exceeds 300, if advance parties in other European capitals are included.

The exact cost of the Reagan trip may never be known. White House officials, sensitive about the image of spending abroad during a recession at home, have declined to give formal estimates. The costs--including the expenses of a small armada of helicopters, limousines and other vehicles--are buried in the budgets of half a dozen different agencies.

When Reagan honored the request of the widow of slain U.S. military attache, Lt. Col. Charles R. Ray, and posthumously promoted him to the rank of full colonel last week, he did so over the opposition of U.S. military bureaucrats who pointed out that Ray was not on the promotion list when he was murdered here by terrorists on Jan. 18.

"Well, he was sure on somebody's list," said Reagan in reference to the terrorists. The president then ordered the promotion.

President Reagan intends to observe Independence Day by greeting returning astronauts July 4, when the space shuttle is scheduled to touch down at Edwards Air Force Base in California before an estimated crowd of 100,000 persons. Edwards is conveniently located a short helicopter flight from the Reagan ranch northwest of Santa Barbara, where the president will take another short holiday the first week of July. He plans to spend three weeks at Rancho del Cielo in August.

Look for a summer offensive on "women's issues" from the Reagan administration. One day before the start of the summit, the "women's question" dominated a White House senior staff meeting in Paris, with the discussion triggered by a new in-house survey which shows the president's already low standing among women voters slumping even further.

During the campaign, and much of the first year of the administration, the big negative among women voters was a widespread perception that Reagan would be too quick to go to war. The president has defused much of this concern, but it has been replaced by another one. The survey shows that Reagan's big negative now is the economic issue, especially among single women who have lost their welfare checks, a category significantly larger than the "welfare cheaters" who are a favorite target of presidential rhetoric.

The Paris breakdown in communications between Secretary of State Alexander M. Haig Jr. and high-ranking White House officials, including national security affairs adviser William P. Clark, uncovered wounds that have never fully healed in the long internecine conflict between Haig and the White House staff . . . . Haig's differences with Defense Secretary Caspar W. Weinberger are well known, but distrust of the secretary of state now expands to another Reagan favorite, Treasury Secretary Donald T. Regan. At a briefing before the European trip, Regan's blunt candor about U.S. difficulties in Europe contrasted with Haig's verbose defense of everything the Reagan administration had done. After the briefing, Regan remarked to an aide that he was never going to participate in a joint briefing with Haig again.

Economic summit participants will exhange French grandeur for California rusticness at next year's summit in Pebble Beach . . . . It's a far cry, culturally as well as geographically, from Versailles, where the host French delegation has sometimes looked askance at American insistence on the creature comforts they enjoy back home. The day before the summit opened, a California reporter touring the grounds remarked scornfully about the limited number of toilets at Versailles, where chemical facilities have been brought in by trailer. "This is a chateau, not Yankee stadium," his French guide told him