The word “pastoral” means to give spiritual guidance. Parents are usually the first to carry out this function, in a childs life. A good example of this is that they arrange the Sacrament of Baptism for their children. Then, follow through with the childs religious education… etc. So, it seems logical that parents DO have “pastoral authority”.
I’m not sure about the blessing part, though. If the Franciscan priest meant, “blessing” in the same sense that a priest or deacon blesses… I don’t think it would be the same thing, for a parent. Because priests and deacons are consecrated by Holy Orders. A parent can certainly “bless” their child in a general sense… such as praying and providing for them… or correcting them, when necessary; but I don’t think it would be the same type of blessing you’d receive from a priest or deacon.
I hope someone more knowledgable will reply. God bless.