Under Louisiana law, specifically La. R.S. 23:921, a Louisiana employer has protection from all but "bad faith" refernces. "Bad faith" for purposes of the statute requires proof that the information was knowlingly false and deliberately misleading. If you have video of the incident for which you were terminated you have a good chance at proving this. Obviously, other corroborating evidence and witnesses would be essential. Without evidence of this nature, you will almost certainly not be successful in a civil suit against them. One possibility is to have a friendly business call and make a record of the exact details of what the former employer is saying about you, which may be so extreme that it is easier to meet the high burden for this type of claim.
In my experience most employers are not vindictive, but there are some, and with the protection afforded by this statute they can do a lot of damage, exactly as you have described. The foregoing is intended as legal information concerning the question asked, but is not intended as legal advice upon which the requesting party may rely in guiding their actions. Rather, the requesting party should consult an attorney for a personal consultation and advice for a full consideration of their situation and rendition of legal advice. Additionally, by providing this general information I am not accepting any representation of the requesting party and I am specifically declining to form an attorney-client relationship with the requesting party unless agreed to later after further consultation and agreement.
Areas of practice listed are are areas of concentration in my practice. I am not board certified in any of the listed areas, and by listing them and describing my practice I am merely describing my experience and the nature of my practice.