In a statement, Spanish Prime Minister Mariano Rajoy said the arms cache move signalled the "definitive defeat" of Eta, blamed for 829 deaths dating back to 1968.
Describing the separatist organisation as "terrorists", Rajoy reiterated the group could expect no government favours as a result and "still less, impunity for their crimes".
"The only logical response to this situation is (for Eta) to announce its definitive dissolution, to apologise to its victims and to disappear rather than mount media operations to disguise its defeat," said a government statement.
Madrid added it would not make an "evaluation" of the weapons arsenal until French authorities have neutralised eight caches of weapons containing 120 firearms and three tonnes of explosives in the southwestern Pyrenees-Atlantiques department bordering Spain.
French Interior Minister Matthias Fekl earlier described the move to hand over remaining arms as a "major step".
In 2011, Eta announced that it had abandoned its armed campaign, but did not give up its weapons. It also continued to insist on amnesty talks for some 360 jailed group members, 75 of them in France.