Good question. Simply put, we don't know, since that has never happened. (And they never allow all those people to be in one place, there's always a cabinet member stashed somewhere else) I imagine the assistant secretaries would take charge of their own departments as acting secretaries (Even though they couldn't go up and into the presidential line of succession) and then the state governors would appoint Senators, which they do in time of an emergency. I imagine then the majority party would decide on who the new president of the Senate would be, and then he would become president by default. I'm pretty sure House seats can only be filled by special election, so the Senate route would probably be faster.Thanks!
And what happens if they all die up to the Secretary of Homeland Security?
Oh! From you link, we can see on the left in the language "Simple English". What's that? American??
The French system is different. If the president dies, the President of the Senate acts as interim president, and cannot hold the office more than 50 days, as the first round of new elections has to be organized 20 to 35 days after the death of the former president.
In case the President of the Senate dies also, in theory the government (prime minister first, then the ministers in the order they appear in the decree creating the government) can make the interim.
But it is very unlikely, because the President of the Senate dies, the Senate would simply elect a new President of the Senate among themselves, and he would act as the interim president.
The main difference is in the US, you cannot have election anytime, you need to wait for the next election year with the vice president being the boss.
Our system as an advantage: the president doesn't have to select someone much worse than him as vice president, so people think twice before trying to assassinate him.
That's just my semi-educated guess, though. I'm not a Constitutional scholar, but I'm pretty sure there is no actual procedure - they'd probably figure something out, though, probably along the lines I outlined above.