Fairfax County moved a small step closer last week to becoming the third major jurisdiction in the Washington area to approve a cable television franchise system.

At a public meeting, county staff members heard industry objections to parts of the proposed county ordinance that would govern cable TV in Fairfax. More than a year remains before Fairfax homeowners outside Reston can expect to have cable TV brining first-run movies into their homes. Reston is now the only area of Fairfax that has cable TV.

Last week's session was a small part of the process of fine-tuning the ordinance, first proposed in July. It is slated to come before the Fairfax Board of Supervisors again Jan. 14. The board is expected to require three or four weeks of advertising before a mid-February hearing, said Ron Mallard, director of the county Department of Consumer Affairs.

If the board then adopts the ordinance, another five or six months will be spent advertising for bids from cable television companies and evaluating proposals, Mallard said.

The ordinance would carve Fairfax County into three franchise areas. A study issued last April recommended dividing the county in half and said that cable television in the sprawling, 366-square mile jurisdiction was only "marginally feasible." The study said that dividing the county would help attract bids from cable firms because it would reduce the amount of money needed to install the system.

Prepared by a Washington consulting firm, Malarkey, Taylor and Associates, the study said Fairfax County is not an attractive area for cable television because of county requirements for underground cable construction in many areas and because a large number of television stations can be received without cable.

Nonetheless, after last week's meeting, a representative of Warner Cable Corp. said the company is considering the three franchise areas with some interest. Soon the change its name to Warner-Amex Cable Communications Inc., the company has offered cable television in Reston -- one of the three franchise areas -- since 1969.

Warner officials asked for the meeting last week to voice their concerns about a draft of the ordinance which they said could jeopardize the company's Reston operation. Richard R. G. Hobson, an attorney with Boothe, Prichard and Dudley, representing Warner, objected to a section of the draft that forbids cable companies from operating without a county franchise, 90 days after a single franchise is awarded.

If the county approved a franchise for the southern or northern section of Fairfax, that would start a 90-day countdown, forcing Warner out of business in Reston unless it received a franchise for the planned community by that time, Hobson said.

"We are looking at modifications to that section that will allay their (Warner's) concerns, but satisfy the interests of Fairfax County," Mallard said after the meeting.

A successful cable television system is operating in neighboring Arlington County, with the rate for regular service set at $7.95 a month, and Home Box Office, featuring movies and special sporting events, for an additional $16.90.

Alexandria became the second area jurisdiction to award a cable franchise last June. The system is expected to be in operation by 1981.

The housing density in both jurisdictions is more than twice that of Fairfax County.

Cable television was developed in the 1950s for use in remote areas that could not receive direct telecasts. With the promise of movies and programs not available through broadcast airwaves, cable spread to more heavily populated areas, reaching about 14 million homes last year, or 19 percent of the nation's 76 million households with television sets.