1. You should have never agreed to be engaged to her if you did not want it as no law can force a person to be a victim of one sided love by some one else.
2. What is the FIR relating to? What charges have been leveled against you in FIR?
3. What has she stated in the affidavit the attestation whereof has been done by magistrate? Has she clearly stated in the affidavit that she does not want further action to be taken in consequence of FIR?
4. The affidavit given by her is not the only basis on which you can move to HC for quashing of FIR. Since the FIR itself is false it is a fit case where you can opt for quashing by High Court. Even if FIR is cancelled by police now on the basis of her affidavit it can again be lodged and/or reopened on the basis of a subsequent complaint by her which she may attempt to lodge if you decide to call of the engagement, whereas FIR once quashed by HC will be conclusive and final for all practical reasons unless she challenges the judgment of High Court in the Supreme Court. The prospects of an appeal being made to SC in a case of this nature are very less.
5. She can take no legal action against you in the event you call off the engagement. As I mentioned earlier no one can be forced to marry a person.