Was Santa Fe founded by Spaniards?

Yes it was. The site of Santa Fe was occupied by Indian Pueblos established from 1050 to 1150, or 500 years before the Spanish took it over as the center of their new Province. The Nambe Pueblo is about 18 Miles north, the Picuris Pueblo is in the Sangre de Cristo mountains Southeast of Taos, the Pojoaque Pueblo is about 15 miles to the north and the San Ildefonso Pueblo is another eight miles beyond. The Oke-Owingo Pueblo where the Spaniards first settled was given the name San Juan by Governor Onate to honor John the Baptist. Santa Clara and Tesque as well as the Taos Pueblo also played a role in selecting Santa Fe as the site for the new government.