What does it mean that someone managed to live beyond 120 years?

In Genesis, the lifespans of people - denoting from birth to death - are described in the following manner, "...the days of [so-and-so] were [number of] years, and he died..." The exception being that of Enoch "...and he was not, for God took him." Later on, Pharoah asks Jacob, Joseph's father, "How many are the days of the years of your life?" The difference here being Jacob hasn't yet died, and the question adds the necessary words, "are" and "of your life?" It's interesting that God uses the same idiom for "man". God: "...yet his days shall be 120 years."

Before God determined that immense decrease in lifespan for the human race (no specific time frame was given for when this would begin to happen to our race), there had been no common maximum lifespan for the human body, other than people seemed to die short of a thousand years; I read in amazement the news some years ago, that scientists discovered the approximate, NATURALLY optimum lifespan capable within the human body is 120 years. Obviously, God can alter this in specific instances for certain individuals, for His own purpose, as He alters other ordinances of His occasionally (such as Enoch being spared the common sentence of physical death of all humans). Granted, few of us - what with poor diet, toxins around us that weaken our immune systems, and warfare - are able to live to that maximum lifespan, even though it exists.

Notice the wording of:

Genesis 6:3 (NLT) 3 Then the LORD said, “My Spirit will not put up with humans for such a long time, for they are only mortal flesh. In the future, their normal lifespan will be no more than 120 years.”

The verse only says "In the future". That could be at anytime God wanted. Look at humans today. How many humans live to 120? Heck you are lucky to make it to 90.

Also this scripture is pre-flood. This is what God said before he decided to wipe them off the earth. When God feels regret, it is not in the sense that God made a wrong decision he regrets. Instead what that means is “change one’s mind with regard to past (or intended) action". God felt regret then when he found favor in Noah. He could also have felt "regret" over his decision to shorten mans life. If God had wiped wickedness off the earth then there would be no need to administer such a punishment.

It's all relative, of course. Here's the immediate context:

When Lamech had lived 182 years, he fathered a son and called his name Noah, saying, “Out of the ground that the LORD has cursed, this one shall bring us relief from our work and from the painful toil of our hands.” Lamech lived after he fathered Noah 595 years and had other sons and daughters. Thus all the days of Lamech were 777 years, and he died.—Genesis 5:28-31 (ESV)

Compared to Lamech, Mme. Calment died regrettably young. She ought to still be in prime of her life.

However, the NET Bible footnote offers a simpler solution:

Heb “his days will be 120 years.” Some interpret this to mean that the age expectancy of people from this point on would be 120, but neither the subsequent narrative nor reality favors this. It is more likely that this refers to the time remaining between this announcement of judgment and the coming of the flood.

Further, we can see that Genesis contradicts the idea that 120 years is a hard limit:

These are the generations of Shem. When Shem was 100 years old, he fathered Arpachshad two years after the flood. And Shem lived after he fathered Arpachshad 500 years and had other sons and daughters.—Genesis 11:10-11 (ESV)

The ages do drop fairly rapidly. Nine generations later:

The days of Terah were 205 years, and Terah died in Haran.—Genesis 11:32 (ESV)

Assuming a limit to the length of life is meant, the author(s) of Genesis seem to be thinking in terms of approximations or orders of magnitude. An occasional 122 (or 130) year-old is to be expected, but we don't see anyone living 500+ years anymore.