The manners to translate this verse are very variegated, but, maybe the correctness of it depends from a lot of factors.
As regards - for example - around the concept of the term 'flesh' [בשׂר], we may find 4 different translating manner, at least ("is flesh", NET Bible, etc.); "is also flesh" (KJV, etc.); "he is but flesh" (NAB, etc.); "he indeed is flesh" (Darby, etc.).
My own in-progress-translation is:
"'[...] my flux of energy [רוח] will not keep under control [ידון] humans until an unsighted time [עלם]. So the days of their contravening [שׁגם] as fleshly beings [בשׂר] will amount to 120 years."
In every case, the best manner to translate the Bible is to take on account also the global context of the Bible itself. So, Bible passage like Job 33:4 and Isa 42:5 indicate that the man's existence in life depends not only from the acceptance of the 'authority' of the countless earth's bio-physical cycles, but also to receive the God's flux of energy [רוח].
Now I cite the fine comment drawn by the Commentary of Keil & Delitzsch (bold is mine): "רוּהַ is the divine spirit of life bestowed upon man, the principle of physical and ethical, natural and spiritual life. This His spirit God will withdraw from man, and thereby put an end to their life and conduct. בְּשַׁגָּם is regarded by many as a particle, compounded of בְּ, שַׁ a contraction of אֲשֶׁר, and גַּם (also), used in the sense of quoniam, because, (בְּשַׁ = בַּאֲשֶׁר, as שַׁ or שֶׁ = אֲשֶׁר Jdg_5:7; Jdg_6:17; Son_1:7). But the objection to this explanation is, that the גַּם, “because he also is flesh,” introduces an incongruous emphasis into the clause. We therefore prefer to regard שַׁגָּם as the inf. of שָׁגַג = שָׁגָה with the suffix: “in their erring (that of men) he (man as a genus) is flesh;” an explanation to which, to our mind, the extremely harsh change of number (they, he), is no objection, since many examples might be adduced of a similar change (vid., Hupfeld on Psa_5:10). Men, says God, have proved themselves by their erring and straying to be flesh, i.e., given up to the flesh, and incapable of being ruled by the Spirit of God and led back to the divine goal of their life."
Similarly does the famous translator Chouraqui: "Dans leur égarement".
As regards the specific point about the '120 years' is very interesting what Jerome said in his Quaestiones Hebraicae in Genesim: "Non igitur humana huita, ut multi errant, in CXX annos contracta est, sed generationi illi CXX anni ad poenitentiam dati sunt". In other words, Jerome believed the 120 years weren't an individual life limit God-given to each man, but a time period for men to do penance.
After that years, the Flood...