Thanks for your question Ben - as you mention, it is a really important issue.
But to put it quite simply, your friend seems to be misinformed.
Constantine was a Roman emperor in the fourth century AD. He was a supporter of the Christian church, reversing the approach of preceding emperors who persecuted the church. One of his significant actions was to gather church leaders from around the Roman empire to a meeting (the ‘Council of Nicea’ in 325AD) to deal with a theological issue that was troubling the church at the time. However, he did not write the Bible, or even the New Testament part of the Bible.
The Old Testament part of the Bible was a recognised collection of scripture before the time of Jesus - a collection that Jesus himself considered to be the word of God. The individual ‘books’ of the New Testament were written during the first century AD by the Apostles of Jesus, or students of the Apostles, and gathered together into a single collection over the ensuing two centuries. Jesus through the ministry of his life, death and resurrection trained, empowered and authorised the Apostles, by the Holy Spirit, to be witnesses to him as the Word of God, and the New Testament is their testimony. All this took place well before the time of Constantine.
Now in the same way that Jesus was an historical figure, the Apostles were historical people - they lived at a particular time and place in history. It follows that their ministries, with the writings that came out of their ministries, bear the markings of the history in which they took place. This does not make the New Testament any less the word of God - it is just that God spoke to real people in real situations.
The same God is concerned for us in our particular situations and he continues to use the Bible to reveal himself and his will to us.
If you want to learn more ...
There is an interview about the legacy of Constantine you can see here Constantine’s Legacy
The following article responds to a claim similar to the one your friend made “Is the Bible True?”
For more detail about the writing of the New Testament and its historical reliability as a witness to Jesus Christ you could have a look at the book “The Christ Files” by John Dickson (also available as a DVD), or “Is The New Testament History?” by Paul Barnett
Hope this clears up the confusion.