St. Thomas Aquinas notes in the Summa Part III that Christ assumed a perfected human nature from the moment of conception, the grace of union preceding habitual grace, both of which are present in Christ. It is incorrect to say that he assumed a “fallen” human nature, since that would entail that He assumed original sin. He did not. Further, to say that Christ “had a fallen nature” is to say that “he was fallen” and this is clearly incorrect. Parenthetically it is important to remember that the true nature of humanity is not “fallen,” it is not. This is a Protestant notion. The true nature of humanity, and our true destiny, is perfection and the beatific vision.
As far as sin, Christ was not conceived via carnal generation, which is necessary for the assumption of original sin. Christ was possessed of the beatific vision from the moment of His conception and therefore was not capable of actual sin either. For Him to be capable of sin, He would have had to have a “fallen nature,” which He did not. Christ was impeccable, i.e. incapable of sin. Christ had no sin nor did he have the fomes of sin. (Summa Theologica, Part III, Q.15, A.1-2.)
There is a nice summation of some of these points by Thomistic scholar Fr. Reginald Garrigou-Lagrange at
thesumma.info/saviour/saviour45.php.