I´m not a Spanish member, but I´ll answer anyway, because I spent some time in the Basque country, incidentally during the 98 World Cup.
It´s true the locals there care much more about their Basque Clubs than about the national team. Especially the Athletic Club of Bilbao is beloved for their policy of employing exclusively Basques. One favourite chanting in the stadium used to be "Ya somos trés/sólo falta el Alavés" - "There´s three of us already/Only Alavés is still missing", meaning that the Athletic, the Real Sociedad de San Sebastián and Pamplona were already playing in the Primera División, while the Club Deportivo Alavés of Vitoria was in Segunda. Now that the Alavés is in Primera as well, that chanting is a little outdated.
They were not that sad when Spain was eliminated, but they do watch the games and cheer for the Basques in the team. Therefore, they also favoured France to win the title, because of their compatriot Vincent Lizarazu playing in that team.