MADISON COUNTY, N.C. -- Along the French Broad River, which courses southward from the Tennessee border to Asheville, temptations lurk: vistas of old homesteads and barns, unspoiled and undeveloped mountains that are part of the southern Appalachians, straight-talking citizens, and a network of rural communities with such names as Upper Shut-in, Bend of Ivy and Paw Paw.

In 1980 Drs. Louis Schroeder and Janice Coverdale, recently married and medical-school graduates, took in all of this. They were hiking the 2,000-mile Maine-to-Georgia Appalachian Trail, which runs through Madison County's western rim. The mountainous area and its people proved to be irresistible. Two years later, after looking over sites in Maine, Kentucky and West Virginia as possibilities to set up their practices, the two physicians -- Schroeder an internist, Coverdale a pediatrician -- decided they would settle here. They've had no regrets since.

At the Marshall-Walnut Medical Center this afternoon, Schroeder is caring for a woman with congested lungs, an asthmatic patient and a man with bursitis. Three children are in the waiting room. Coverdale is at a nearby clinic in Mars Hill.

The story of two young physicians choosing a low-paying rural practice in an isolated part of North Carolina is rare enough. U.S. medical schools aren't producing an overflow of independent-thinking doctors heading for the hills.

A greater unusualness is that four years ago, the citizens of Madison County decided to stop applying for federal and state money to run their community-health programs. They were grateful for past subsidies, but the need for independence began to override the desire for governmental backing.

''You have to understand that people in these parts believe powerfully in self-sufficiency,'' says Prof. Tom Plaut, a sociologist at Mars Hill College, a liberal-arts school whose 1,000 students equal 50 percent of the town's population. ''There was a feeling, too, of uncertainty. The government's rug could be pulled out at any time. We would never know from one year to the next about the grants.''

In 1986 Schroeder, Coverdale and a group of other doctors borrowed $500,000 from a local bank to buy a building in Mars Hill from which a countywide medical fee-for-service program was run in four nonprofit health centers. They pledged to keep their salaries low and be fair-minded with patients too poor to pay. With citizens involved through a community-based board, the program is making it.

''It's a challenging practice,'' says Coverdale. ''We aren't here as missionaries. We're here because this is first-line medicine. Then, too, this is beautiful land and a good place to raise a family.''

Last year, the W. K. Kellogg Foundation, established in 1930 to ''help people help themselves,'' awarded a $1.1 million grant to the Madison County program, with the purpose of learning how a community-oriented approach to rural health care can bolster traditional kinds of care. The grant was made in part because of such settled-in doctors as Schroeder and Coverdale, and because the 17,000 citizens of Madison County, as independent-minded as they may be, remain trapped in rural poverty. The isolated townships were medically underserved.

Many of the citizens who come to the four centers -- for about 36,000 visits a year -- are health-care poor. They are part of the U.S. poverty population, which is only 40 percent covered by Medicaid, down from 63 percent in 1975, according to the Catholic Health Association. Twelve million children are uninsured, about one-third of the total.

In Madison County, as elsewhere in rural America, the working poor find themselves caught between high private insurance rates and ineligibility for public assistance. The Center on Budget and Public Priorities reports that in 1987 the poverty rate for rural families in which the head of the family worked was 10 percent -- up nearly a third in 10 years. The poverty rate among all working families in rural areas is double that for urban, areas. Madison County took a pummeling in 1986, when a shoe factory closed, with 435 jobs lost -- nearly 40 percent of the county's total.

Despite the harshness, families endure. They are strengthened by communal cohesiveness based on a mountain culture of mutual aid. That also is part of what brings -- and keeps -- some young doctors here.