"Nous avons droit à un personnel administratif."
Could this be better expressed as "We have the right to one administrative person"
No. "Une personne" is something different than "un personnel", which really translates as "staff".
You would not say AN administrative personnel in English. You would say "administrative personnel"
Does this sentence in French refer to something specific, like a lawyer? And does 'un personnel' refer to a staff (a body of staffers) or to one person? If just one person, I would translate as 'right to an administrative staff person.'