I was largely just wondering about this as there are a number of very fun, interesting things that could be done with the character.
Mary Shelley's Frankenstein is indeed public domain so you are free to use that character.
However, a lot of what we think of as "Frankenstein" is not Mary Shelly, for example, the iconic Frankenstein look dates from the 1931 film which may still be under copyright.
You can use elements that are public domain, you can't use elements that aren't.
