When Jean Smith leaves today for Europe and Asia with her husband, Attorney General William French Smith, her spot on the rented Air Force jet will be paid for by the Justice Department.

"She's going 'space available,' " said Art Brill, deputy director of public affairs at the Justice Department. "Her presence will contribute to the objectives of the trip. All additional expenses will be paid for by the Smiths."

The attorney general's objectives are to check into international refugee, drug-trafficking and terrorism problems in France, Italy, Pakistan, Thailand, Japan and Hong Kong--the most extensive foreign trip an attorney general has ever taken, according to Brill. "A dollar spent in a source country is worth tens of dollars spent here," he said. "We have to try."

Jean Smith's objective is to talk up the 8-year-old White House Fellows Program with officials in all those places except Hong Kong.

"I asked her to," says her old friend, United States Information Agency director Charles Wick, who calls his invitation to Smith part of his American Participants program, which utilizes American citizens traveling abroad to tell foreign audiences how great the United States is.

President Reagan, another old friend, named her to the nonpaying 31-member White House Fellows Commission shortly after he took office. Since then, Smith says, she has been impressed by the amount of foreign interest shown in the program.

"Ultimately, the great thing would be if an exchange program of some sort were developed. But for now, people just want to know about setting up their own," she says.

Meanwhile, Brill said, "she will enhance the official functions of the trip." The Justice Department's legal counsel, consulted on the propriety of payment, cited the controller general's opinion of Nov. 27, 1981, that a spouse can enhance the trip and therefore fly at government expense. Jean Smith will do her part by standing in on a couple of social occasions for the attorney general.

"You know," says Brill, "it's customary for Cabinet and sub-Cabinet wives to go along with their husbands on trips abroad."