The Karoo, South Africa - But officers are slowly building profiles of Philippe Pierre Meniere, 60, and Agnes Jeanne Jardel, 55, with the little information available to them.
Police have even deployed local farmers to help in the search.
"We got farmers to take police to possible hiding places in the area," said police spokesman Lieutenant-Colonel Hendrik Swart.
On Friday, the two allegedly opened fire on policemen and Cobus and Jaen du Plessis, whose father owns the Sutherland house they occupied. One officer died and another was wounded in the back.
The two, who Cobus du Plessis said were Ramtha School of Enlightenment members, fled with guns and food. Details on the two, who lived like hermits on the farm for more than 10 years, are sketchy.
"There are few pictures available of them, for example," said Swart. "We managed to dig out two pictures from the house.
"But the one was probably taken 10 to 15 years ago We are still working hard to get more information."
Swart said the two were definitely not married, despite numerous reports that they are. "They are from France but have South African identity documents."
Meniere, who is 1.82m tall and slender, has spectacles, and was last seen wearing hiking boots, South African National Defence Force pants and a shirt.
"He [speaks] English with a strong French accent. He is qualified as a medical doctor in France and did undergo some military training in France," said Swart.
Jardel is 1.7m tall, slender and has long grey hair. She was wearing SANDF clothing and hiking boots.
"At the moment we know very little about her. I we don't know what she did for a living," said Swart. Cobus du Plessis told The Times she said she worked in advertising and marketing.
When police raided the farmhouse they found unregistered weapons. After the shoot-out with police they fled with four pistols, a rifle and a shotgun.
Swart said the pair was dangerous and appealed to the community to be on the lookout. "The community is also requested not to confront the suspects if found, but to immediately contact their nearest police station," said Swart.