I'm sorry to hear about this. If you're comfortable with sharing, could you give us a bit of high-level background as to why you were fired?
Given that your former firm said “no” it sounds like this was due to something you did on your end, as opposed to restructuring?
If so, there's not much you can do. If your new firm asks you to explain the situation you need to do so very very carefully. I highly recommend you craft your answer, practice answering, and make sure you're as neutral as possible.
Honestly, it wouldn't hurt to get a coach to help “pressure test” you and roleplay out the call with HR.