By tournament:

1955 Madrid University Sevens
1987 Benidorm / Costa Blanca Sevens

The list may be subject to change if more rugby union sevens tournaments are discovered.

Madrid University Sevens

From The Official History of the Melrose Sevens by Walter Allan:

The first sevens tournament was held at Madrid University at 1955.

Benidorm Sevens

The first Benidorm Sevens tournament was staged in 1987. It was won by the Scottish side Gala Y.M.