The arrests took place without violence although a weapon was subsequently found in the car, a police source said.
Michele Alliot-Marie, the French interior minister, confirmed the arrests and named the man as Asier Eceiza Ayerra, one of six Eta suspects featured on wanted posters distributed at the beginning of the year.
Alliot-Marie said he was a senior official in Eta’s military leadership, but gave no details on the woman suspect.
Spain’s RNE radio said Ayerra was believed to be the deputy of Txeroki, the head of Eta’s military command.
Spanish police suspect Ayerra planned a July 2003 attack that left 13 injured in hotels in Benidorm and Alicante in southern Spain.
He has been on the run since 2002, according to RNE.
Spanish media identified the arrested woman as Olga Gomez Arambilez, a suspected member of a recently dismantled Eta cell.
Meanwhile on Friday, police found another weapons cache belonging to Eta in northern Spain, a source close to the investigation said, in the third such find this week.
The cache was found in Getxo, a suburb of the Basque financial capital Bilbao, the source told the AFP news agency.
Police on Thursday found over 100 kilograms of explosives, as well as several detonators and French and Portuguese licence plates, in a cache belonging to Eta near the northern town of Santo Domingo de la Calzada in the province of La Rioja.
A day earlier police found a cache containing an automatic rifle, tools to steal cars and a box of tranquilisers in the nearby ski resort of Valdezcaray.
The discovery of the weapons follows the arrest on Tuesday of nine suspected members of Eta’s Vizcaya cell, including Arkaitz Goikoetxea, its leader.
Police on Thursday detained a 10th person suspected of belonging to the cell in Getxo.
The Vizcaya cell was planning to stage a major attack in Getxo and kidnap a Basque politician belonging to the Socialist party of Jose Luis Rodriguez Zapatero, the Spanish prime minister, according to Spanish media reports.
Eta is blamed for the deaths of 823 people in its 40-year campaign of bombings and shootings to carve a Basque homeland out of northern Spain and southwestern France.