For though only those predestined to salvation receive the light of faith and truly feel the power of the gospel, yet experience shows that the reprobate are sometimes effected by almost the same feeling as the elect, so that in even in their own judgment they do not in any way differ from the elect [c/f Acts 13:48]. Therefore it is not at all absurd that the apostle should attribute to them a taste of the heavenly gifts [Heb 6:4-6] and Christ, faith for a time [Luke 8:13]; not because they firmly grasp the force of the spiritual grace and the sure light of faith, but because the Lord, to render them more convicted and inexcusable, steals into their minds to the extent that his goodness may be tasted without the spirit of adoption. 
It would appear that what Calvin is saying is that people may exhibit all the outward signs of being elected, but inwardly they are without the Spirit of God and therefore not a child of God. The vital attribute of faith is the inward working of the Spirit. In talking about faith and knowledge Calvin speaks of both our knowledge of the word of God and acceptance of its promises and the work of the Holy Spirit in opening up our hearts in testimony to those truths. Calvin puts it like this:
Our mind must be otherwise illumined and our heart strengthened that the word of God may obtain full faith among us. Now we shall possess a right definition of faith if we call it a firm and certain knowledge of God’s benevolence towards us, founded upon the truth of the freely given promise in Christ, both revealed to our minds and sealed upon our hearts through the Holy Spirit. 
This is the backbone of Calvin’s understanding of assurance. True faith is a firm and CERTAIN knowledge of God’s mercy towards us, appropriating the sure promises of God in Christ as revealed through the Holy Spirit. Beeke writes:
Thus for Calvin assuring faith compels an indissoluble tie between saving knowledge, the scriptures, Jesus Christ, God’s promises, the work of the Holy Spirit and Election…Calvin is arguing that faith involves something more than fully believing the undoubted promise of God objectively; rather it contains personal, subjective assurance. 
There is no dichotomy between saving faith and assurance.
However, one problem still exists. If the reprobate can have all the outward signs of the elect, how can the elect know that they are saved?
 Ibid pg 555
 Ibid pg 551
 Beeke pg 49