The Fauquier County Board of Supervisors yesterday won a federal court battle to force payment of a $350,000 insurance claim for funds the county paid a woman who was severely burned in a 1980 fire at the county jail.

The woman, Virginia Hitt, who was permanently disfigured in the fire, received $350,000 from the county in an out-of-court settlement last summer. Under terms of yesterday's court ruling in the county's suit against its insurance carrier, the Harleyville Mutual Insurance Co. of Richmond, another $150,000 will go to Hitt and the remaining $200,000 to the county.

The fire started when Hitt, arrested on a drunk driving charge, threw a match on a cell mattress, according to trial testimony.

"The county's decision to settle with Hitt last summer was not only reasonable but extremely prudent," District Judge Albert V. Bryan Jr. said yesterday after a one-day, non-jury trial in Alexandria.

He noted that after last summer's settlement, Hitt unsucessfully sued Fauquier County Sheriff Luther Cox and a former jailer. Bryan yesterday called that jury verdict "a surprise" and said the earlier suit could have cost the county more than $2 or $3 million if officials had not decided to settle it.

Bryan rejected the argument of lawyers for the insurance company that the board's liability coverage had been allowed to lapse through negligence by county officials.

Lawyers for the company contended that Fauquier officials had allowed their policy to lapse before the fire because it appeared to duplicate other coverage for the county's supervisors. The county maintained it acted on the advice of a Harleysville agent and Bryan agreed.