Today the Basques are as matriarchal as every community in Europe: not very much (matriarchal = matrilineal + matrilocal). Nevertheless you will find here matriarchal elements, like in all European societies. You can follow the traces in religion (Christianity in most of Europe), the folklore, tales and legends, habits and traditions, especially at festivals.
Though, the Basques are speaking their own non-indoeuropean language, which means, the cultural influence from the patriarchal Kurgan Culture had less influence on them as on other European peoples, i.e. the Greeks or Celts or Germans.