When Attorney General William French Smith left early last week for a three-week, around-the-world trip, he and his traveling party totally depleted the Justice Department's travel fund, according to lawyers who asked for travel money and discovered the cupboard was bare.

Department officials say the shortage was temporary -- just for a day or two -- and that lawyers with emergency travel needs were sent on an interim basis to the Washington office of the U.S. Marshal Service to get funds.

In briefings before Smith left Oct. 19, officials refused to say what the trip would cost.

But since then, the Air Force has estimated that the military plane carrying the attorney general and the traveling party will cost more than $370,000. That does not include the cost of hotels, meals and the many FBI agents sent along as bodyguards for the dignitaries.

Art Brill, a spokesman for the department, said yesterday that the travel fund was emptied about Oct. 15 when Smith and eight members of his traveling party took about $10,000 in cash -- $1,300 each -- from the fund. He said additional funds were transferred from the Treasury Department within one or two working days the next week.

"This is absolute nonsense," Brill said of the complaints by some of the lawyers. "I'm told that no travel was inhibited . . . they're making a mountain out of a molehill."

Brill said that at worst some employes may have had to wait a day or two to collect on expense accounts or to be repaid for local taxi fares.

When government employes travel, they are provided with plane tickets. In addition, when traveling within the country they normally get cash advances of $75 a day to use for hotel and meal expenses.

The temporary shortage in travel money did result in some grumbling by lawyers who said they resented having to run around town to get cash to pay expenses for immediate court appearances "while the attorney general is on a round-the-world trip with all the advance money."

In a briefing before Smith left, government officials said Smith would be visiting Japan, Hong Kong, Thailand, Pakistan, Paris and Rome to meet with foreign officials.

They said he would discuss such problems as narcotics trafficking, refugee camps, terrorism and the theft of trade secrets.

Those officials refused to say exactly who would be going on the 22-day trip. Besides Smith, the travel roster included Francis Mullen, head of the Drug Enforcement Administration and Alan C. Nelson, commissioner of the Immigration and Naturalization Service.

Smith's wife Jean also is traveling at government expense. An official said that her travel expenses had been okayed because she planned to do do some work for the U.S. Information Agency, which is headed by Charles Z. Wick, a long-time friend of the Smiths.

According to one Justice Department employe, "There's been an incredible amount of bitching at the FBI about the agents they took along for protection--when some of us can't get money for investigations ."

An FBI spokesman said that for security reasons he could not say how many agents are along. Brill said yesterday that the decision was made to use military rather than commercial aircraft because of the security risk.

"There's a grave security risk over there, believe me," he said. "The security people were firm against taking commercial travel, especially given the history of airport incidents."

He also complained about the bad publicity the attorney general's trip has received, pointing out that two top priorities of the department are drug trafficking -- which produced $79 billion a year in illegal profits -- and the refugee problem.

Brill added that because of Smith's close and longstanding friendship with President Reagan, he will wield much more influence in these foreign countries than other visiting officials.

"I just think some of that should come out, too," he said.