Response: Two issues are presented by your question: (a) whether the last will is valid in the sense that the court will accept it for probate in New Jersey and (b) whether it is a self-proving will that can be admitted into probate without the need to get affidavits from the witnesses to the will's execution. As to the first question, the fact that you were in Florida when the will was executed although residents of New Jersey should not, by itself, effect the legality of the will. New Jersey probate law sets for the following as the rule for a legal last will.
3B:3-2. Formal execution of will. Except as provided in N.J.S. 3B:3-3, every will shall be in writing, signed by the testator or in his name by some other person in his presence and at his direction, and shall be signed by at least two persons each of whom witnessed either the signing or the testator's acknowledgment of the signature or of the will.Note that it is not necessary for the will to be notarized in order for it to be valid.
Although having the will notarized is not necessary for a valid will, it is necessary to make the will self-proving. It may or may not be difficult for you locate the witnesses to the will in order to secure affidavits from them (which will be necessary if the will is NOT to be self-proving). On this point, the question is whether a notary licensed as such in the State of Florida is a proper officer before whom to execute a New Jersey last will so that it will be accepted into probate in New Jersey. I don't know the answer to that question. As always, the best course of action is to take the will to a local attorney experienced in probate administration for an opinion on the matter. I hope the foregoing was helpful in some way.