Francisco was born in Santiago, Chile. He studied to become a Doctor of Law.
According to historian Diego Barros Arana the government of Barreda was as short and irrelevant. During his government the cabildo of Santiago sent a request to the viceroy of Perú to have Mauricio de Zavala confirmed as governor of Barreda until the arrival of titular governor Bruno, who had to arrive to Chile through Buenos Aires. Zavala would never have this position. The news about some Dutch ships which had cast anchor in the neighborhoods of Valdivia spread and they arrived to governor Barreda. He sent 200 men to avoid a disembarkation and to avoid possible smugglings.
He inaugurated the Caja de Recogidas, a work begun by Gabriel Cano, in Santiago. This institution worked as an asylum and jail of women at the same time.
The government of Barreda ended when the viceroy José de Armendáriz, Marquis of Castelfuerte, decided not to confirm him and instead appointed as governor a member of the army, the Maestro de Campo of the army in Chile, Manuel Silvestre de Salamanca Cano.
After his death, his family became poor.