Catholics believe the books in their Bible are inspired because they were handed on by Christ’s apostles to the Church to be read in the liturgy as Sacred Scripture.
There have been times throughout Church history when the inspiration of certain books has come into question. At these times, the Magisterium of the Church (guided by the Holy Spirit) would come together and make a decision about the canon of Scripture. The Major Church Pronouncements on the Bible can be found here:
catholicapologetics.org/ap031100.htm
You should point out to your students the example set in Acts 15 when the Apostolic Church, guided by the Holy Spirit, settled the first major controversy in the Church. The same method the Apostles used then is still used today and was used to settle the canonicity of Scripture. The Holy Spirit revealed the inspiration of the books of the Bible through the direction of the Magisterium of the Church–the bishops in union with the bishop of Rome.
You might find this online book helpful:
Where We Got the Bible: Our Debt to the Catholic Church
by The Right Rev. HENRY G. GRAHAM,
catholicapologetics.info/apologetics/protestantism/wbible.htm
(This book is available in print as well.)
Many of the Council documents cited above (Council of Carthage, Florence, and Trent) are available online if you want to see the lists of which books the Church accepted.
Also, you can read the articles about the NT and OT canon in the Catholic Encyclopedia:
newadvent.org/cathen/03267a.htm
newadvent.org/cathen/03274a.htm