Centeno, 24, who had been on a routine counter-terrorist surveillance operation with French counterparts at the time of his death, was saluted by King Carlos, Zapatero and other dignitaries as he was buried.
Centeno and colleague Fernando Trapero had stopped at a cafe for coffee in the small port of Capbreton and found themselves a few tables away from three Eta suspects, Michele Alliot-Marie, France's interior minister, said.
Alfredo Perez Rubalcaba, Spain's interior minister, said the two groups recognised each other and after a verbal exchange in the car park the Eta suspects shot both guards.
Centeno died at the scene. Trapero, 23, is "in a coma without any indication of brain activity," Angel Piquemalle, spokesman for the Cote Basque hospital in Bayonne, said.
Zapatero's government came under pressure when peace talks with Eta stalled last year.
Since then, Spain has taken a hard line towards the group, its political wing Batasuna, and entities seen as lending support to them.
Thousands of protesters marched through the city of Bilbao in northern Spain on Sunday in favour of "rights for all in the Basque country" and "democracy for all political options".
The demonstrators were protesting against the Spanish high court's detention order for 46 members of Basque pro-independence groups for their alleged links with Eta.
|Signs carried by protesters read "Rights for|
all in the Basque Country" [Reuters]
In a bid to increase the pressure on Zapatero's government and force concessions, Eta has staged more than half-a-dozen nonfatal attacks since August.
The separatist group declared a cease-fire in March 2006 but grew impatient with slow progress in talks with the government.
It killed two people in a car bombing at Madrid airport in December 2006, and declared the truce formally over in June. Centeno was the third fatality since December.
Eta has killed about 800 people since the late 1960s in a bid to establish an independent Basque state in ancestral lands which straddle a western section of the Spanish-French border.