The biggest things he has going for him were
a) A national profile. The Federalists don't have many well known figures on the national level and for better or worse Pinckney - who is well known for his role dealing with France during the Quasi-War - is all they have with Adams retired, Hamilton Dead and Chief Justice John Marshall refusing to seek the presidency.
b) His role in the XYZ affair paints him as staunchly anti-French and tacitly pro-British which is still an appealing talking point. His resolution to this whole affair would likely be to pursue tighter relations with Britain as long as the US was free to stay out of the Napoleonic wars.