Enock's faith is similar to Abel's. Enock had no more scripture than Abel had. That is beyond the light of nature, they only had the words of Adam and Eve. We might overlook how powerful that scripture was. Fresh after creation and the fall, and living with the very same people who originally fellowshipped with God, the evincing nature of their words would strike faith like a match to any heart open to God. Hearing directly from Eve God's promise of salvation in 'crushing' the Devil's head, seems enough to explain primative, yet lively faith.
But more to the point of Enock's 'walk with God', I assume the idea can be traced to this:
8Then the man and his wife heard the sound of the
LORD God as he was walking in the garden in the cool of
the day, and they hid from the LORD God among the
trees of the garden. 9But the LORD God called to the
man, “Where are you?” (Genesis 3:8-9)
From these verses it could be argued that God used to fellowship with Adam and Eve, appearing to them in the garden in some shape, possibly even in human form, as they heard him 'walking'. Possibly God the Son was visiting them and already manifesting an image of His future form? In any case, whatever form this was, it seems that Adam and Eve would then 'walk with God'. When we look for our friends and do not find them where they usually are, we say 'Where are you?' This, therefore, indicates 'walking with God' was fellowshipping with Him and enjoying His presence.
So it would seem to me that Enock had a very lively faith by beleiving in the promise of salvation and that was enough for Enock to experience God's presence. That is, Enock sensed God in his life and enjoyed God very much. God was so pleased with Enock by his unusual faith that He took Him. So Enock not only stands as an oustanding example of faith, but represents the first idea that salvation inlcudes a physical ressurection of the material body, by that same faith. Enocks faith was like a lightenng bolt from heaven.
In this interpretation I assume fellowship is related to enjoyment, and enjoyment is integral with love. Enock's faith and love are therefore how he 'specifically pleased God'.