Then was Jesus led up of the Spirit into the wilderness to be tempted of the devil.  And when he had fasted forty days and forty nights, he was afterward an hungred.  And when the tempter came to him, he said, If thou be the Son of God, command that these stones be made bread.  But he answered and said, It is written, Man shall not live by bread alone, but by every word that proceedeth out of the mouth of God.
This is what I've been able to come up with on the connection between this passage and Noah:
The devil hates humanity and indeed all of creation, and the last thing he wants is for the Incarnation to succeed. He, the evil one, 'invented' enmity between God and man, and there's no way he's going to let the Godman abolish it. So he comes to Jesus Christ, who is hungry after 40 days of fasting, thinking, Hmm, hungry... this'll be easy. I'll do it just like last time! I'll get him to sin with food.
He wants Jesus to sin like Adam, so that He will die like Adam, and God's purpose will be thwarted.
The significance of the 40 days then, is huge, especially
as it relates to Noah and the flood. The end of the flood is the beginning of a 'new' creation, the old having been wiped out. So, too, is Jesus' temptation the beginning of the new creation. The 40 days and 40 nights help to establish Christ as the new and better Adam.
Unlike the first time around, when Adam sinned by transgressing the commandment and eating the forbidden fruit, in the new creation, Jesus Christ refuses to listen to the devil and to turn the stones into bread. Perhaps this is part of the reason why our liturgical hymns specifically mention that Adam sinned by failing to fast?