Dutch Morial, the maverick who became this city's first black mayor in a low-budget campaign four years ago, is seeking reelection Saturday as a solidly financed, entrenched incumbent who is supported by much of the city's establishment.

Five men are opposing Morial's bid for a second four-year term, but only two, state Sen. William Jefferson and state Rep. Ron Faucheux, are considered "serious" candidates. Morial, Jefferson and Faucheux (pronounced Fo-SHAY) are Democrats. Faucheux is white and Jefferson is black.

Political pollsters see Morial and Faucheux running neck and neck, and Jefferson is viewed as the candidate who could draw enough votes from each to throw the contest into a runoff March 20.

This is an open primary election, in which candidates from all parties seek election at the same time. Morial is expected to get a heavy black vote, while Faucheux is expected to draw much of the white support. Approximately 55 percent of New Orleans' 240,054 voters are white, and 45 percent are black.

Morial, who legally changed his given name, Ernest, in favor of his nickname, defeated a host of establishment candidates four years ago, but he has been courting establishment support in this campaign.

As a result, he has won the endorsement of black political organizations and the approval of a business club that used to be a bastion of white men. And a former leader of this city's best-known, most socially prestigious Mardi Gras organization has done a television commercial for the mayor, praising him as a strong leader.

In his campaign, Morial, 52, has amassed about $1.1 million in campaign money, far ahead of Faucheux' $436,673 and Jefferson's $226,118. In his 1977 campaign, Morial spent only $300,000.

Much of this money has been used to plaster buses and billboards with messages hailing Morial as a man who can get streets repaired, squeeze money from the legislature, lure new industry and jobs here and, above all, be tough.

Sometimes, though, his aides and opponents say, this toughness goes too far and turns into arrogance and, occasionally, temperamental fury. This happened in a December forum, when he wound up shouting at Jefferson.

Faucheux and Jefferson have attacked Morial for what they call his lack of leadership after the November, 1980, killing of four blacks by policemen hunting the slayer of a white officer.

Jefferson charged that Morial's performance demoralized the police, and Faucheux faulted Morial for "his absence of presence in this issue."

The mayor has retaliated by describing the two as "outsiders looking in."

While Morial has emphasized his accomplishments, his two major opponents have come up with proposals in two sensitive areas: the economy and crime.

Faucheux, 31, who has stressed anticrime legislation during his six years in the legislature, has promised to get tougher with criminals.

And Jefferson, 34, a first-term state senator, has stressed money, saying that New Orleans will have to generate more revenue because the Reagan administration seems an unlikely source of federal dollars.

Jefferson's solution is radical. In a city where massive exemptions keep all but about 15 percent of property owners from paying taxes, Jefferson has proposed a referendum on cutting back exemptions.

According to a recent poll, Morial had 39.4 percent of the vote, Faucheux had 34.9 and Jefferson had 8.6.

When he won four years ago, Morial received 90 percent of the black vote and 20 percent of the white vote, primarily from upper and middle classes. But Morial pollster Edward F. Renwick said about 30 percent of those voters now are undecided.

"Where that vote goes could, to a large extent, determine who will be mayor," he said.