A promising experiment in urban renewal slowly is transforming the worn face of this old manufacturing and oystering town, where vacant storefronts and faded tenements are giving way to chic restaurants, art galleries, woodworking shops and leather makers.

The depressed south side of Norwalk has become one of the nation's first "enterprise zones," a local version of the federal proposal that President Reagan has been trying for two years to push through a skeptical Congress.

Through a mixture of tax incentives and cash grants, officials here have saved nearly 1,000 jobs by persuading a number of businesses to remain in the city or expand their facilities. They have had less success in attracting new companies, however, and they insist the zone cannot work without support from the more traditional federal aid programs.

"The enterprise zone is not a panacea that will solve all urban problems," said Michael Lyons, a Republican city councilman who is the program's chief advocate. "But it's a really valuable tool for an urban area that is sort of on the edge, rather than one that's already burned out. It uses a conservative view of how the market works to achieve liberal goals."

Twenty-one states have adopted varying kinds of enterprise zones, which have opened for business in seven states, including Connecticut. These local zones have become something of a grass-roots movement, with their own national association and a bimonthly newsletter.

The Senate has passed the Reagan proposal twice, but it recently was dropped from a conference committee after House Democrats refused to vote for it. The Democrats agreed, however, to hold the first House hearings on the measure this fall.

The Reagan bill would allow the secretary of Housing and Urban Development to designate 75 federal zones, where businesses would be eligible for federal tax credits for investment, expansion and hiring the disadvantaged. Some Democrats have expressed concern about the lost revenue and question whether the concept will work; others say they don't want to provide a political windfall for the administration or give Reagan an excuse to cut more direct urban aid programs.

Meanwhile, a number of cities are angling for an inside track on any future federal effort. New Orleans has designated 94 enterprise zones, some as small as a city block, which have helped create 475 jobs by luring two high-technology firms, one of them from California's Silicon Valley.

Baltimore, which, along with Hagerstown, has one of two zones operating in Maryland, has limited its zone to a 40-acre industrial park. Control Data Corp. has renovated an empty school there and rented out most of the space to new companies. Virginia and other states hope to designate zones in the coming months.

Here in Norwalk, a coastal community of 78,000 about 30 miles northeast of the Bronx, Lyons and his colleagues campaigned hard for the plan in becoming the first Republicans to run the city in 18 years. Last fall, they made Norwalk the first of five designated cities in Connecticut to open a zone.

"We suffered from the typical old Northeast industrial city syndrome," said Lyons, 28. "Many businesses wanted to expand, but they were deciding to leave because of the general decline of the area. Everyone just figured the place would sink into depression."

Under the program, companies that locate or expand in Norwalk's one-square-mile zone get 80 percent off their local property taxes for five years and a 50 percent break on state business taxes for 10 years. The firms also get a $1,000 cash grant for every full-time job they create, so long as one-third of the new hires are disadvantaged local residents.

Unlike the federal bill, moreover, companies also can receive state job-training funds and low-interest venture capital loans, an effort to provide seed money for struggling firms that have little use for tax benefits.

Hoffrel Instruments will be the first business in the zone to receive the training grants for hiring 20 new workers. The 80-person firm, which makes ultrasonic cardiovascular scanners that can detect blocked arteries without surgery, considered leaving town last year when it decided to expand.

But the zone's new benefits helped convince company officials to rebuild the third floor of their 40-year-old factory, which had been occupied by a firm making handwoven purses.

"The tax breaks were one of the main attractions that caused us to consider staying here in town," said Hoffrel official John McGeorge. "It's pure gravy. This isn't the fanciest neighborhood in the world, but there's a good pool of skilled labor here. I thought this part of town was going right down the drain, but now people are moving back into the neighborhood and putting up vinyl siding and mowing the grass."

Furniture store owner Irving Avrick didn't want to rebuild his warehouse after it burned down, but he changed his mind after learning of the tax abatement. "For nine or 10 years I've got a free ride," he said. "Now how the hell can I turn that down?"

Lyons hopes the South Side neighborhood, which has the city's greatest concentration of minority residents and run-down public housing, will make use of another zone benefit: interest-free loans to renovate residential property.

For now, many developers are focusing on Washington Row, a historic preservation district where workers are hammering, sanding and painting the brick facades. The street will include a Mexican restaurant (El Acapulco), an 1890s-style bar (Jeremiah Donovan's), a formal wear shop (Merit Tux 'n Tails), a jewelry store (Marshall Arts), an art gallery (A Thousand Words) and a new condominium (Haviland Arms) where units are selling for up to $90,000.

All the new construction is bothering several older stores that aren't receiving any tax breaks. "They should be helping someone who's hanging in here," said Bob Malkin, owner of Fox Hardware, whose business has dropped more than 25 percent. "I'm the one who's probably suffered the most on this street."