Edwin Edwards is Louisiana's cure for boredom. He is also its governor and has been since 1971, except for the four years he had to take off between 1979 and 1983 because the state constitution would not let him serve three consecutive terms. The voters wanted to be entertained again, so they brought him back. And now, starting Tuesday in Room 468 of the U.S. District Court here, the man known as Fast Eddy will be part of a show that is more than the people bargained for and certainly beyond what the governor planned to give them.

They are calling it Louisiana's trial of the century, a racketeering case that matches Edwards, undefeated at the polls, against U.S. Attorney John Volz, unbeaten in the courtroom. The hyperbolic billing comes in part because sitting governors don't often face criminal charges (Edwards is No. 6); partly because there is a need for diversion in a state that has turned nasty and depressed from oil and gas busts and World's Fair flops; and partly because there is a sense that this trial might prove historic.

It could see the passing of an era that began with Huey P. Long, the Kingfish, shot to death 50 years ago last week in the marble skyscraper state house he built as a monument to himself, and filtered through a line of brothers and sons down to Edwards, unrelated but still descendant, heir to an irresistible Louisiana mix of populism, humor, demagoguery and cronyism.

On the eve of the long-anticipated trial, there is a feeling here that Edwards might have done something shady but that he will probably beat the rap. Even law professors who privately consider Edwards at best a rapscallion and at worst a sleaze, think that he is so smart that he likely found a way to do what he did just inside the borders of the law or, failing that, that he is so entrancing that the trial will end with a hung jury.

Edwards is accused, in a 50-count indictment, of conspiring with his brother Marion, who is dying of liver cancer, a nephew and a band of lawyers, architects and business buddies in an illegal hospital-certification scheme that brought the governor about $2 million. The indictment charges that the enterprise was conceived while Edwards was out of office and carried out upon his return and involved concealment, coercion, promises of promotion and fraud.

Edwards acknowledges that he made the money. He denies that he broke the law.

Since the indictment, the governor has behaved as though he were waging another political campaign, berating his opponent -- in this case prosecutor Volz, a former Democrat who switched parties shortly after President Reagan took office. By Edwards' account, Volz is the point man in a partisan effort to get him by a "vicious, cynical and heartless group of people" in a party controlled by "neo-Nazis and arch-conservatives."

It is a line of defense to which Louisianians have grown accustomed. Twelve years ago it was used by Volz's old boss, former New Orleans district attorney Jim Garrison, who was indicted on charges that he took bribes from the pinball industry. Garrison, who spent much of his career trying to prove that the Central Intelligence Agency killed President Kennedy, said his indictment during the Nixon administration was political. "It is an honor," he said, "to be prosecuted by the most corrupt administration in the 200-year history of this country."

Garrison was acquitted and is a state appeals court judge. He said Volz, who was his chief of staff in the district attorney's office, is an aggressive prosecutor but not politically motivated. "And I say that even though I'm very, very fond of Edwin Edwards," Garrison said. "I think he's been an awfully good governor."

Volz and Edwards have been under a gag order imposed by Judge Marcel Livaudais, but that has hardly kept their battles out of the news media. Their most important dispute arose over what they said to each other during a preindictment meeting Jan. 2 in Volz's office. Volz told the grand jury that Edwards offered to resign to avoid indictment. According to a transcript of the grand jury proceedings, Volz recalled his meeting with Edwards this way: "He Edwards said, 'I will do anything to avoid being indicted.' He said, 'I'll resign.' He said, 'Would that make any difference?'

"I said, 'I can't make that kind of an agreement with you.' I said, 'I can't just make that kind of an agreement.' He said, 'I don't want it brought on the state.' He said, 'I can't tell you what this is going to do to the state if I'm indicted.' He said, 'It's going to bring down all kinds of bad publicity. If I have to go to jail, that's secondary to what's going to happen to the state.' "

Edwards disputed Volz's account. "What I said is, 'If you could show me where I violated the law, I'll gladly resign and take whatever sentence the judge gives me,' " Edwards said. "He Volz could not do that." Edwards and his attorneys asked Livaudais to throw out the case on the grounds that Volz acted improperly when he appeared before the grand jury as both prosecutor and witness describing the meeting with the governor. The dismissal motions were denied.

When not questioning the motives of the prosecutors, Edwards has been wooing the voters of southeast Louisiana, mindful that among them are the 12 people who will decide his fate. He has been making five to 10 appearances a week, including two on this final pretrial weekend at a highway dedication and a hospital.

The most recent statewide opinion polls were taken in March, shortly after the indictment. Those showed that Edwards, who was reelected in 1983 with 62 percent of the vote, had lost about half his support within one year.

University of Loyola pollster Ed Renwick, who conducted the surveys, said he has taken some private, local polls recently that show about the same situation.

"Edwards is down to his core constituency, but he's still doing extremely well among those groups, labor and blacks," Renwick said. "The people here are very tolerant of political chicanery. It's a Louisiane cliche, but it happens to be true. Imagine having one-third of the electorate sticking with you on these kinds of charges."

The jury-selection process, which begins Tuesday, promises to be among the more revealing and perhaps lengthy aspects of the case. The 16-lawyer defense team -- led by Nashville's James F. Neal, who was the special prosecutor during the Watergate coverup trials -- has prepared thick forms full of psychological and political questions for the potential jurors. Defense attorneys may be further aided by Livaudais' decision to allow lengthy, individual questioning of potential jurors.

The elaborate defense, which has already featured mock juries listening to Edwards' defense in suburban Jefferson Parish, will be funded by the governor's many friends and contributors who have been sending money to a defense fund run by E.C. Hunt, a Lake Charles lawyer/developer. Hunt has known Edwards since 1953, when they were young lawyers in the French-speaking Cajun territory of southwest Louisiana who negotiated insurance settlements and shared an addiction to malts and fruit sodas.

Hunt thinks he might be in the defense-fund business for the long haul. Even if Edwards is acquitted this time, as Hunt expects, he will probably be indicted again, Hunt thinks. "Back in the War of 1812, they used a lot of grapeshot, which was just junk -- chains, fences, stones, anything they could find to stick into the cannon and fire. Well, the prosecution is firing grapeshot at Edwin hoping that something, someday will hit him. They'll fire again if they miss this time. He's such a target."

Hunt is among those, friend and foe, who say they believe that Edwards is simply too smart to have knowingly broken the law.

"There are two things Edwin doesn't want to do. One is die, and the other is go to jail," Hunt said.

"Let me tell you a story about that. This one time, during his first term, there were 20 of us at a lunch at the governor's and as we were sitting there, one fellow up and said, 'Govnuh, if you'll get me access to this interchange I need for a store I'm fixin' to build, I'll give you $100,000 in cash, hear?' Now this is an uneducated man. There are 20 people at the table. And Edwin says to him, 'I know you want this project, and I'm sure it's a good project, but what you're saying to me could get us both in a great deal of trouble. It would be wrong for you to give me the money and wrong for me to take it. Anyway, if you're going to give me $100,000 in cash, please don't do it in front of 20 witnesses.' "

That is a classic example of Edwards' style. He has a way, said his press secretary, Meg Curtis, of "making people forget the seriousness of things."

Edwards has spent a career joking about the women he's seen, the bets he's played, the troubles he's had and escaped from. And his glib, seductive ways may serve him well as he enters a courtroom as a criminal defendant.

Shortly after his indictment, Edwards boasted that he was the best lawyer he'd ever seen and that he would present his own summation to the jury. There has been less boasting of that sort lately. As the governor put it, in a different context -- a ribbon-cutting ceremony Friday in the heat of a brilliant fall morning: "I have a lot that I'd like to say. But I'm going to save it for a cooler day."