Presidential Succession - Foreign Born Cabinet Members?

[Robespierre's Jaw]

So what happens if the President, Vice President, Speaker of the House, Senate Pro Temp and most cabinet members die tragically on the same day. However, the only remanding surviver is the foreign born (in this scenario) Secretary of State.

What happens? Does the Secretary of State become President of the United States? Or does someone entirely different becomes President?

[True Federalist (진정한 연방 주의자)]

Under current law, we'd be without a President until either a Speaker or PPT was chosen.