The two suspects, who were both armed, were arrested in the southern French village of Chateauneuf de Randon, a police source said.
Jose Luis Rodriguez Zapatero, Spain's prime minister, said he was pleased to hear of the arrests.
"These members of the terrorist group Eta are probably the authors of this attack," he told a news conference after a Spanish-Italian summit in Naples.
"It's important that the state of law gives a rapid response with the arrest of the two likely authors."
More than 1,500 police officers had hunted across France for three attackers since Saturday's shooting.
The Spanish Civil Guard officers had been on a routine anti-terrorist surveillance operation Saturday with French counterparts at the time of the shooting.
The police officers and the Eta suspects recognised each other in a café and, after an exchange of words in a car park, the suspected Eta members shot both Spanish guards, Spanish officials said.
Raul Centeno, 24, was killed instantly. Trapero had been in a coma at a hospital in Bayonne in southwest France before his death.
The first Eta killings in almost a year have highlighted the Spanish government's policies in the Basque region before general elections due in March.
The opposition Popular party has attacked Zapatero's approach to the conflict after government peace talks with the separatist group failed last year.
More than 800 people have died in conflict between Eta and Spain since the group began its struggle for independence for Basque territories in northern Spain and southern France four decades ago.