Final answer:
The enzyme DNA polymerase is responsible for attaching free-floating nucleotides to the DNA molecule during replication.
Step-by-step explanation:
The enzyme that helps attach free-floating nucleotides to the DNA molecule during replication is DNA polymerase. This enzyme plays a critical role in adding nucleotides one-by-one to the growing DNA chain that is complementary to the template strand. DNA polymerase synthesizes the new strand of DNA by adding nucleotides in a sequence determined by the original DNA strand, ensuring the fidelity of DNA replication.