Whether or not your contract is admissable in court depends on many factors, mostly related to how reliable it is. The notarization helps prove that your ex-fiance's signature is genuine, and if necessary you could get the notary as a witness to verify their notarization. That notarization would seem to make it hard for him to deny that the contract is genuine and his signature on it are genuine.
But the admissibility in court is a separate issue from whether it's enforceable. In California, the requisite factors include the capacity of the parties to contract, a legal purpose, material terms set out, etc. etc.
You should have a lawyer review the document to get a better answer of your chances in a lawsuit.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship. .
A notary's stamp is not worth the $5 you paid to get it. It only means that the signature on a document is your signature. It does not mean the document is genuine or legal or that it will be admissible in Court.
As previous answers said, the admissibility depends on the document and the proceedings.
That said, if the amount is $3,000 and you do want to proceed with suit, you can file in small claims court (claims for $3,000 or under can do so). You will not be able to have an attorney represent you if you do so, but the small claims procedures can take less time than filing in district court.
Please feel free to contact me if you would like to discuss the matter further.