Francisca in 1542 had married Álvaro de Zúñiga y Sotomayor, 4th marquis of Gibraleón, 6th count of Belalcázar (died 24 February 1559).
This name Zúñiga belonged to her husband's mother, "Teresa de Zúñiga", who died 25 November 1565, 2nd marchioness of Ayamonte, Lady of Lepe and Redondela, 3rd duchess of Béjar on her own rights, 4th countess of Bañares, 2nd marchioness of Gibraleón.
Her husband, a "Sotomayor", from Córdoba, was also a member of the nobility but not as wealthy or as important as his wife.
Once more, the inherited name was not necessarily always "transmitted" by the father exclusively, things depending on personal circumstances.
Francisca died without issue too, in 1597, and her ducal titles passed to her nephew, the son of her sister Beatriz, Antonio Fernández de Córdoba y Cardona (1550–1606).