Police said the car was sitting on the track near the Northwest Community Center on Samuel Drive when the east-bound train struck it.
Identity of those involved had not been released pending notification of next of kin of the 44-year-old woman.
Witnesses told police the Chrysler 300 was idling on the track, its driver talking with the driver of another also on the track, when the other driver apparently saw the train and moved off the the track.
The driver of the Chrysler did not, despite the whistle blaring from the approaching train, witnesses said.
The driver was taken to the Eunice Police Department, where toxicology tests were being administered. Officers said he was suspected of being legally drunk.
Witnesses said the man, formerly of Eunice, they said, was participating in activities of a trail ride which was assembled at the Northwest Center pavilion.
The injured passengers, young adults, were taken by air to trauma centers.