In a statement sent to Basque language paper Berria, the group "EH ez de salgai" (The Basque Country is not for sale) said it had set fire to the house in Hélette, near the Spanish border, because it was "only used a few weeks of the year".
On the day after the attack, the 30 May, the couple, who live in the Spanish city of Pamplona, said they "were extremely attached to the Basque cause" and had planned to live in the house after their retirement.
House prices are a hot-button isssue in the French Basque Country and the attackers said that "the only way to respond will be to take action against second homes and estate agents".
"It seems very serious to us that a family from the Basque Country has a second home while knowing about the housing problem," their statement said.
The slogan "The Basque Country is not for sale" was painted on a wall at the scene of the arson attack and has been seen at the scenes of previous attacks.
The statement has been sent to anti-teror police in Paris.