We can't exactly see Victor singing "Born This Way" (but we like to imagine it). At the same time, that's basically his anthem: over and over, he tells us that he just couldn't help it. It was destiny. It was fate. He was meant to discover the secret of life. Great! So, Frankenstein definitely agrees that we're born to certain paths; we're controlled by our genes (or whatever they thought of as genes in the early nineteenth century), and we just can't help it.
Not so fast. First, Percy Shelley's revision to the 1831 edition made fate way more important than it was in the original 1818 edition (source). Second, there's the whole issue of the monster, who seems to make some pretty clear choices about his behavior. Sure, he blames his looks and his dad and, well, everyone he encounters. But does that mean he didn't have a choice?
In Frankenstein, people are masters of their own destinies. Victor only blames fate because he's looking for an excuse.
No one in Frankenstein can be held responsible for his actions, because fate is stronger than free will.